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flow of fluids.pptx

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snehapachore2

This document provides information about fluid mechanics and fluid flow. It discusses topics such as fluid statics, fluid dynamics, types of fluid flow, Reynolds experiment, the Reynolds number, Bernoulli's theorem, manometers, and methods for measuring the rate of fluid flow. Some key points include: - Fluid statics deals with fluids at rest while fluid dynamics examines fluids in motion. - The Reynolds number is a dimensionless number that can be used to predict laminar or turbulent flow. - Bernoulli's theorem states that the total energy per unit mass of a fluid remains constant in steady, incompressible flow. - Manometers such as simple, differential, and inclined manometers can be used to

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Ms. Sneha A. Pachore
A fluid is a substance that continually deforms (flows) under an applied shear stress Fluids are a subset of the phases of matter and include liquids, gases Fluid flow may be defined as the flow of substances that do not permanently resist distortion & continually deforms (flows) under an applied shear stress At a given temp & pressure a liquid possesses a definite density In case of gases the density is affected by both temp & pressure The subject of fluid flow can be divided into fluid statics and fluid dynamics
FLUID STATICS Fluid statics deals with the fluids at rest in equilibrium Behavior of liquid at rest Nature of pressure it exerts and the variation of pressure at different layers Pressure differences between layers of liquids A fluid, like water or air exerts a pressure on its surroundings. This pressure applies a distributed load on surfaces surrounding the fluid, like the face of a dam Study of flids at rest is based on 2 principals: 1. Pressure at point is same in all direction 2. Pressure is same in all direction in a horizontal line in a continuous fluid description: 1. Consider a column of liquid with two openings which are provided at the wall of the vessel at different height 2. The rate of flow through these opening s are different due to the pressure exerted at the different height 3. Consider a stationary column the pressure ps is acting on the surface of the fluid, column is maintained at constant 4. pressure by applying pressure
FLUID DYNAMICS Fluid dynamics deals with the study of fluids in motion or nature of fluid flow This knowledge is important for liquids, gels, ointments which will change their flow behavior when exposed to different stress conditions like i. Mixing ii. flow through pipes iii. filled in container Fluid dynamics Bernoullis theorem, flow of fluids in pipes, laminar and turbulent flow.
TYPES OF FLOW- Identification of type of flow is important in Manufacture of dosage forms Handling of drugs for administration The flow of fluid through a closed channel can be viscous or observed by Reynolds experiment Glass tube is connected to reservoir of water, rate of flow of valve, a reservoir of colored solution is connected to one end of help of nozzle. Colored solution is introduced into the nozzle as fine stream Laminar flow is one in which the fluid particles move in layers layer sliding with other. There is no exchange of fluid particles When velocity of the water is increased the thread of the and mass of the water gets uniformly colored, indicates complete mixing of the solution called as turbulent flow The velocity at which the fluid changes from laminar flow to is called as critical velocity
FLUID DYNAMICS REYNOLDS EXPERIMENT This experiment was performed by Osborne Reynolds in 1883. a glass tube was connected to a reservoir of water in such a way that the velocity of water flowing through the tube could be varied. At the inlet end of the tube a nozzle was fitted through which a fine stream of coloured water can be introduced. After experimentation Reynolds found that when the velocity of the water was low the thread of color maintained itself through the tube. By putting one of these jets at different points in cross section, it can be shown that in no part of the tube there was mixing, and the fluid flowed in parallel straight lines. As the velocity was increased, it was found that at a definite velocity the thread disappeared, and the entire mass of liquid was uniformly colored. In other words the individual particles of liquid, instead of flowing in an orderly manner parallel to the long axes of the tube, were now flowing in an erratic manner so that there was complete mixing.
Types Of Flow in Reynolds Number 1. Laminar flow is one in which the fluid particles move in layers or laminar with one layer sliding with other There is no exchange of fluid particles from one layer to other Avg. Velocity = 0.5 Vmax Re < 2000 2. Turbulent flow is when velocity of the water is increased the thread of the colored water disappears and mass of There is complete mixing of the solution and the flow of the fluid is called as turbulent flow Avg velocity = 0.8 Vmax Re > 4000 The velocity at which the fluid changes from laminar flow to turbulent flow that velocity is called velocity
flow of fluids.pptx
THE REYNOLDS NUMBER From Reynolds experiment it was found that critical velocity depends on or Reynolds number is obtained by the following equation In Reynolds experiment the flow conditions are affected by 1. The internal diameter of the tube , m (D) 2. The average velocity of the fluid, m/s (u) 3. The density of the fluid, kg/m3 () and 4. The viscosity of the fluid, pa.s (袖) Further, Reynolds showed that these four factors must be combined in one and only one way namely as Reynolds number Re = Du 袖 i.e. Re obtained by following equation, Re = inertial force viscous force Re = mass acceleration of liquid flowing shear stress area This function (Du /袖) is known as the Reynolds number. It is a dimensionless group.
it has been shown that for straight circular pipe, when the value of the Reynolds number is less than 2000 the flow will always be viscous. i. If Re < 2000 the flow, is said to be laminar orviscous flow or streamline flow ii. If Re > 4000 the flow is said to be turbulent iii. If Re lies between 2000 to 4000 the flow change between laminar to turbulent Inertial forces are due to mass and the velocity of the fluid particles trying to diffuse the fluid particles Viscous force if the frictional force due to the viscosity of the fluid which make the motion of the fluid in parallel. At low velocities, the inertial forces are less when compared to the frictional forces Resulting flow will be viscous in nature Other hand when inertial forces are predominant the fluid layers break up due to the increase in velocity hence turbulent flow takes place.
Applications 1. Reynolds number is used to predict the nature of the flow 2. Stokes law equation is modified to include Reynolds number to study the rate of When velocity is plotted against the distance from the wall following conclusions can be drawn 1. The flow of fluid in the middle of the pipe is faster than the fluid near to the wall 2. The velocity of fluid approaches zero as the pipe wall is approached 3. At the actual surface of the pipe wall the velocity of the fluid is zero 4. The velocity of the fluid is zero at the wall surface there should be some layer in viscous flow stagnant layer 5. if the flow is turbulent at the center and viscous at the surface a buffer layer exist, this buffer viscous to turbulent flow
BERNOULLIS THEOREM When the principle of conservation of energy is applied to the flow of fluids, the resulting equation is called Bernoulli's theorem. Let us consider the system represented in the figure and assume that the temperature is uniform through out the system. This figure represents a channel conveying a liquid from point A to point B The pump supplies the necessary energy to cause the flow. Let us consider a liquid mass m (lb) is entering at point A. Let the pressure at A and B are PA and PB (lb-force/ft2 ) respectively. The average velocity of the liquid at A and B are UA and UB (ft/sec).
BERNOULLIS THEOREM As Considererd a pump working under isothermal/ uniform temperature conditions between points A and B Bernoullis theorem states that in a steady state the total energy per unit mass consists of pressure, kinetic and potential energies are constant Kinetic energy = UA 2 / 2g Pressure energy = Pa / Ag At point A = 1KG of liquid is assumed to be entering at this point, pressure energy at joule can be written as Pressure energy = Pa /g A Where Pa = Pressure at point a g = Acceleration due to gravity A = Density of the liquid
Potential energy of a body is defined as the energy possessed by the body by the virtue of its position Potential energy = XA Kinetic energy of a body is defined as the energy possessed by the body by virtue of its motion, Kinetic energy = UA 2/ 2g Total energy at point A = Pressure energy + Potential energy + Kinetic energy Total energy at point A = PA /g A + XA + UA 2/ 2g According to the Bernoullis theorem the total energy at point A is constant, so Total energy at point A = PA /g A + XA+ UA 2 / 2g = Constant After the system reaches the steady state, whenever 1KG of liquid enters at point A, and another 1KG of liquid leaves at point B Total energy at point B = PB /g B + XB + UB 2/ 2g i.e. INPUT = OUT PUT PA /g A +XA + UA 2/ 2g = PB /g B +XB + UB 2/2g
Theoretically all kinds of the energies involved in fluid flow should be accounted, pump has added certain amount of energy Energy added by the pump = + wJ During the transport some energy is converted to heat due to frictional Forces Loss of energy due to friction in the line = FJ So, Bernoulli's Theorem= Pa /g A +XA + UA 2/ 2g F + W = PB /g B +XB + UB 2/2g OR
Applications 1. Used in the measurement of rate of fluid flow 2. It applied in the working of the centrifugal pump, in this kinetic energy is converted into 3. Used in the measurement of rate of fluid flow using flowmeters. Energy losses According to the law of conversation of energy, energy balance have to be properly calculated Fluids experiences energy losses in several ways while flowing through pipes, they are 1. Frictional losses 2. Losses in the fitting 3. Enlargement losses 4. Contraction losses
1. Frictional losses During flow of fluids frictional forces causes a loss in pressure(Pf pascles) Type of fluid flow also influences the losses i.e either turbulent or viscous. In general pressure drop will be i. Pressure drop 留 velocity of fluid (u) m/s ii. Pressure drop 留 Density of fluid() kg/m3 iii. Pressure drop 留 Length of the pipe (L) m iv. Pressure drop 留/1 diameter of the pipe (D) These relationships are proposed in Fanning equation for Fanning equation: Pf = 2 f2uL / D (viscous/turbulent) f = frictional factor Pf = Pressure drop , Pa Equ considers the friction losses when fluid is passing through straight pipe Value of f depends on: Nature of flow of fluid ( viscous/turbulent) Roughness of inner surface of pipe. For viscous flow H & P equ is employed for calculating pressure drop Hagen Poiseullie equation = 32 Lu侶 / D2 (Viscous flow) Friction losses are permanent , so potential & kinetic energies are converted into heat
Losses in fitting large number of fittings are introduced in pipe during the flow of fluid for long distances. This leads to disturbance in the flow and hence loss of energy. These losses may be either due to change in the direction of flow or change in the of fitting like union couplings or even some valve and meters. Losses in the fittings are expressed in terms of an equivalent length of straight pipe (ELSP) which is in forms of a number as per the diameter of pipe. These numbers are used to convert the fitting in to its equivalent of straight pipe Equivalent length of fitting = ELSP * internal diameter of pipe
Fanning equation is applicable for the losses in straight pipe. When fitting are introduced into a straight pipe, they cause disturbance in the flow, which result in the additional loss of energy losses in fitting may be due to 1. Change in direction e.g elbow fitting 2. Change in the type of fittings e.g. coupling, union, valve fitting etc Tee fitting Equivalent length = 90 Globe valve equivalent length = 300 Equivalent fitting = Equivalent fitting x internal diameter For globe valve= 300 x 50 = 15 meter That means globe valve is equal to 15 meters straight line, so this length is substituted in fanning equation= 300 x 50 = 15 meter
Enlargement loss If the cross section of the pipe enlarges gradually, the fluid adapts itself to the changed section without any disturbance, So no loss of energy If the cross section of the pipe changes suddenly then loss in energy is observed due to eddies. These are greater at this point than straight line pipe Then u2< u1 For sudden enlargement = He = (u1 u2)2 / 2g He= loss of head due to sudden enlargement
flow of fluids.pptx
Manometers Manometers are the devices used for measuring the pressure difference Manometers are used to measure the pressure of any fluid Different type of manometers are there they are 1. Simple manometer 2. Differential manometer 3. Inclined manometer 1. Simple manometer This manometer is the most commonly used one It consists of a glass U shaped tube filled with a liquid A- of density A kg /meter3 and above A the arms are filled with liquid B of density B The liquid A and B are immiscible and the interference can be seen clearly If two different pressures are applied on the two arms the meniscus of the one liquid will be higher than the other Let pressure at point 1 will be P1 Pascal's and point 5 will be P2 Pascal's The pressure at point 2 can be written as = P1+ (m + R ) B g As (m + R ) = distance from 3 to 5
Since the points 2 and 3 are at same height the pressure at 3 can be written as Pressure at 3 =P1+ (m + R ) B g Pressure at 4 can be written as = P2 + gm B or = P1+ B ( m + R ) g - a R g Both the equations should be equal P2 + gm B = P1+ B ( m + R ) g- A R g P1 P2 = gm B - B ( m + R) g + A R g P = gm B - gm B - R B g + R A =R ( A- B )g Pressure difference can be determined by measuring R Manometers are use in measuring flow of fluid
2. Differential manometers These manometers are suitable for measurement of small pressure differences It is also known as two Fluid U- tube manometer It contains two immiscible liquids A and B having nearly same densities The U tube contains of enlarged chambers on both limbs Using the principle of simple manometer the pressure differences can be written as P =P1 P2 =R (C A) g Hence smaller the difference between C and A larger will be R
3. Inclined tube manometers Many applications require accurate measurement of low pressure such as drafts and very low differentials, primarily in air and gas installations. In these applications the manometer is arranged with the indicating tube inclined, as in Figure, therefore providing an expanded scale. i.e. In this type of manometer the leg containing one meniscus must move a considerable distance along the tube. This enables the measurement of small pressure changes with increased accuracy. P1 P2 = g R ( A - B) sin 留 For measuring small difference in pressure this type of manometer is used.
Measurement of rate of flow of fluids Whenever fluid are used in a process it is necessary to measure the rate at which the fluid is flowing through the pipe Methods of measurement are 1. Direct weighing or measuring 2. Hydrodynamic methods Orifice meter Venturi meter Pitot meter Rotameter 3. Direct displacement meter 1. Direct weighing or measuring The liquid flowing through a pipe is collected for specific period at any point and weighed or measured, and the rate of flow can be determined. Gases cannot be determined by this method
Orifice meter Principle Orifice meter is a thin plate containing a narrow and sharp aperture When a fluid stream is allowed to pass through a narrow constriction the velocity of the fluid increase compared to up stream This results in decrease in pressure drop and the difference in the pressure may be read from a manometer The velocity of the fluid at thin constriction may be written as U0 =C 0 2g H H = can be measured by manometer C0 = constant U0 = velocity of fluid at the point of orifice meter Applications Velocity at either of the point A and B can be measured Volume of liquid flowing per hour can be determined by knowing the area of the cross section
Construction It is considered a thin plate containing a sharp aperture through which fluid flows Normally it is placed between long straight pipes For present discussion plate is introduced into pipe and manometer is connected at points A and B Working Orifice meter is referred as the variable head meter, i.e it measure the variation in the pressure across a fixed point construction placed in the path of flow When fluid is allowed to pass through the orifice the velocity of the fluid at point B increase, as a result at point A pressure will be increased. Difference in the pressure is measured by manometer Bernoulli's equation is applied to point A and point B for experimental conditions U02 UA2 =C02g. H U0 = velocity of fluid at orifice UA = velocity of fluid at point A C0 = constant If the diameter of the orifice is 1/5 or less of the pipe diameter then UA is neglected
flow of fluids.pptx
flow of fluids.pptx
When fluid is allowed to pass through narrow venturi throat then velocity of fluid increases and pressure decreases Difference in upstream and downstream pressure head can be measured by using Manometer
Advantage Power loss is less Head loss is negligible Disadvantage Expensive Not flexible it is permanent Need technical export Differentness between or Why Venturi meter if Orifice meter is available? Main disadvantage of orifice meter is power loss due to sudden contraction with consequent eddies on other side of orifice plate We can minimize power loss by gradual contraction of pipe Ventury meter consist of two tapperd (conical section) inserted in pipeline Friction losses and eddies can be minimized by this arrangement ifice and venture meter
flow of fluids.pptx
Pitot Tube Principle: Pitot tube consists of sensing element with a small constriction compared to the size of the flow channel. When the sensing element is inserted at the center of the stream, the velocity of flow is increased. This results in decrease in pressure head. Hp = u2 2g 40
Tube are inserted in the flow shown is the figure U2 = Cv 2g. H Cv = Coefficient of Pitot tube Working of Pitot Tube A pitot tube is simply a small cylinder that faces a fluid so that the fluid can enter it Because the cylinder is open on one side and enclosed on the other, fluid entering it cannot flow any further and comes to a rest inside of the device A diaphragm inside of the pitot tube separates the incoming pressure (static pressure) from the stagnation pressure (total pressure) of a system The difference between these two measurements determines the fluids rate of flow
Advantages: Pitot tubes measure pressure levels in a fluid They do not contain any moving parts and routine use does not easily damage them Also, pitot tubes are small and can be used in tight spaces that other devices cannot fit into Disadvantages: Foreign material in a fluid can easily clog pitot tubes and disrupt normal readings as a result This is a major problem that has already caused several aircraft to crash and many more to make emergency landings
flow of fluids.pptx
Float: Floats may be constructed of metals of various densities from lead to aluminum or from glass or plastic. Stainless-steel floats are common ones Float shapes and proportions are also varied for different applications For small flows floats are spherical in shape Working As the flow is upward through the tapered tube the plummet rises and falls depend on the flow rate Greater the flow rate higher the rise of float Fluid enters the tapered tube, some of the fluid strikes directly the float. Some of the fluid passes from sides Two forces are acting in this case: Upthurst Force (Buoyancy) Weight of the float When equilibrium is established the float comes to rest
Measurement of flow rate The flowrate is measured directly from calibrated scale. The reading is noted generally from ending point of cap of the float. Advantages: No external power or fuel Manufactured of cheap materials Since the area of the flow passage increases as the float moves up the tube, the scale is approximately linear. Disadvantages: Accuracy of rotameter Uncertainty of the measurement Impact of gravity Rotameter is a device used to measure fluid flow, in which a float rises in a tapered vertical tube to a height dependent on the rate of flow through the tube
QUE BANK Define fluids with its properties Differentiate between fluid statics and fluid dynamics Recall the applications of Reynolds number Discuss the types of energy losses Describe the construction and working of simple monometer Compare and contrast between the three types of monometers Point out the devices used for measuring the rate of flow of fluids Explain the principle and working of orifice meter Discuss the construction and working of venturi meter Differentiate between orifice and venturi meter Justify the importance of pitot tube Recall the importance of rotameter as a fluid flow measuring device

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flow of fluids.pptx

  • 1. Ms. Sneha A. Pachore
  • 2. A fluid is a substance that continually deforms (flows) under an applied shear stress Fluids are a subset of the phases of matter and include liquids, gases Fluid flow may be defined as the flow of substances that do not permanently resist distortion & continually deforms (flows) under an applied shear stress At a given temp & pressure a liquid possesses a definite density In case of gases the density is affected by both temp & pressure The subject of fluid flow can be divided into fluid statics and fluid dynamics
  • 3. FLUID STATICS Fluid statics deals with the fluids at rest in equilibrium Behavior of liquid at rest Nature of pressure it exerts and the variation of pressure at different layers Pressure differences between layers of liquids A fluid, like water or air exerts a pressure on its surroundings. This pressure applies a distributed load on surfaces surrounding the fluid, like the face of a dam Study of flids at rest is based on 2 principals: 1. Pressure at point is same in all direction 2. Pressure is same in all direction in a horizontal line in a continuous fluid description: 1. Consider a column of liquid with two openings which are provided at the wall of the vessel at different height 2. The rate of flow through these opening s are different due to the pressure exerted at the different height 3. Consider a stationary column the pressure ps is acting on the surface of the fluid, column is maintained at constant 4. pressure by applying pressure
  • 4. FLUID DYNAMICS Fluid dynamics deals with the study of fluids in motion or nature of fluid flow This knowledge is important for liquids, gels, ointments which will change their flow behavior when exposed to different stress conditions like i. Mixing ii. flow through pipes iii. filled in container Fluid dynamics Bernoullis theorem, flow of fluids in pipes, laminar and turbulent flow.
  • 5. TYPES OF FLOW- Identification of type of flow is important in Manufacture of dosage forms Handling of drugs for administration The flow of fluid through a closed channel can be viscous or observed by Reynolds experiment Glass tube is connected to reservoir of water, rate of flow of valve, a reservoir of colored solution is connected to one end of help of nozzle. Colored solution is introduced into the nozzle as fine stream Laminar flow is one in which the fluid particles move in layers layer sliding with other. There is no exchange of fluid particles When velocity of the water is increased the thread of the and mass of the water gets uniformly colored, indicates complete mixing of the solution called as turbulent flow The velocity at which the fluid changes from laminar flow to is called as critical velocity
  • 6. FLUID DYNAMICS REYNOLDS EXPERIMENT This experiment was performed by Osborne Reynolds in 1883. a glass tube was connected to a reservoir of water in such a way that the velocity of water flowing through the tube could be varied. At the inlet end of the tube a nozzle was fitted through which a fine stream of coloured water can be introduced. After experimentation Reynolds found that when the velocity of the water was low the thread of color maintained itself through the tube. By putting one of these jets at different points in cross section, it can be shown that in no part of the tube there was mixing, and the fluid flowed in parallel straight lines. As the velocity was increased, it was found that at a definite velocity the thread disappeared, and the entire mass of liquid was uniformly colored. In other words the individual particles of liquid, instead of flowing in an orderly manner parallel to the long axes of the tube, were now flowing in an erratic manner so that there was complete mixing.
  • 7. Types Of Flow in Reynolds Number 1. Laminar flow is one in which the fluid particles move in layers or laminar with one layer sliding with other There is no exchange of fluid particles from one layer to other Avg. Velocity = 0.5 Vmax Re < 2000 2. Turbulent flow is when velocity of the water is increased the thread of the colored water disappears and mass of There is complete mixing of the solution and the flow of the fluid is called as turbulent flow Avg velocity = 0.8 Vmax Re > 4000 The velocity at which the fluid changes from laminar flow to turbulent flow that velocity is called velocity
  • 9. THE REYNOLDS NUMBER From Reynolds experiment it was found that critical velocity depends on or Reynolds number is obtained by the following equation In Reynolds experiment the flow conditions are affected by 1. The internal diameter of the tube , m (D) 2. The average velocity of the fluid, m/s (u) 3. The density of the fluid, kg/m3 () and 4. The viscosity of the fluid, pa.s (袖) Further, Reynolds showed that these four factors must be combined in one and only one way namely as Reynolds number Re = Du 袖 i.e. Re obtained by following equation, Re = inertial force viscous force Re = mass acceleration of liquid flowing shear stress area This function (Du /袖) is known as the Reynolds number. It is a dimensionless group.
  • 10. it has been shown that for straight circular pipe, when the value of the Reynolds number is less than 2000 the flow will always be viscous. i. If Re < 2000 the flow, is said to be laminar orviscous flow or streamline flow ii. If Re > 4000 the flow is said to be turbulent iii. If Re lies between 2000 to 4000 the flow change between laminar to turbulent Inertial forces are due to mass and the velocity of the fluid particles trying to diffuse the fluid particles Viscous force if the frictional force due to the viscosity of the fluid which make the motion of the fluid in parallel. At low velocities, the inertial forces are less when compared to the frictional forces Resulting flow will be viscous in nature Other hand when inertial forces are predominant the fluid layers break up due to the increase in velocity hence turbulent flow takes place.
  • 11. Applications 1. Reynolds number is used to predict the nature of the flow 2. Stokes law equation is modified to include Reynolds number to study the rate of When velocity is plotted against the distance from the wall following conclusions can be drawn 1. The flow of fluid in the middle of the pipe is faster than the fluid near to the wall 2. The velocity of fluid approaches zero as the pipe wall is approached 3. At the actual surface of the pipe wall the velocity of the fluid is zero 4. The velocity of the fluid is zero at the wall surface there should be some layer in viscous flow stagnant layer 5. if the flow is turbulent at the center and viscous at the surface a buffer layer exist, this buffer viscous to turbulent flow
  • 12. BERNOULLIS THEOREM When the principle of conservation of energy is applied to the flow of fluids, the resulting equation is called Bernoulli's theorem. Let us consider the system represented in the figure and assume that the temperature is uniform through out the system. This figure represents a channel conveying a liquid from point A to point B The pump supplies the necessary energy to cause the flow. Let us consider a liquid mass m (lb) is entering at point A. Let the pressure at A and B are PA and PB (lb-force/ft2 ) respectively. The average velocity of the liquid at A and B are UA and UB (ft/sec).
  • 13. BERNOULLIS THEOREM As Considererd a pump working under isothermal/ uniform temperature conditions between points A and B Bernoullis theorem states that in a steady state the total energy per unit mass consists of pressure, kinetic and potential energies are constant Kinetic energy = UA 2 / 2g Pressure energy = Pa / Ag At point A = 1KG of liquid is assumed to be entering at this point, pressure energy at joule can be written as Pressure energy = Pa /g A Where Pa = Pressure at point a g = Acceleration due to gravity A = Density of the liquid
  • 14. Potential energy of a body is defined as the energy possessed by the body by the virtue of its position Potential energy = XA Kinetic energy of a body is defined as the energy possessed by the body by virtue of its motion, Kinetic energy = UA 2/ 2g Total energy at point A = Pressure energy + Potential energy + Kinetic energy Total energy at point A = PA /g A + XA + UA 2/ 2g According to the Bernoullis theorem the total energy at point A is constant, so Total energy at point A = PA /g A + XA+ UA 2 / 2g = Constant After the system reaches the steady state, whenever 1KG of liquid enters at point A, and another 1KG of liquid leaves at point B Total energy at point B = PB /g B + XB + UB 2/ 2g i.e. INPUT = OUT PUT PA /g A +XA + UA 2/ 2g = PB /g B +XB + UB 2/2g
  • 15. Theoretically all kinds of the energies involved in fluid flow should be accounted, pump has added certain amount of energy Energy added by the pump = + wJ During the transport some energy is converted to heat due to frictional Forces Loss of energy due to friction in the line = FJ So, Bernoulli's Theorem= Pa /g A +XA + UA 2/ 2g F + W = PB /g B +XB + UB 2/2g OR
  • 16. Applications 1. Used in the measurement of rate of fluid flow 2. It applied in the working of the centrifugal pump, in this kinetic energy is converted into 3. Used in the measurement of rate of fluid flow using flowmeters. Energy losses According to the law of conversation of energy, energy balance have to be properly calculated Fluids experiences energy losses in several ways while flowing through pipes, they are 1. Frictional losses 2. Losses in the fitting 3. Enlargement losses 4. Contraction losses
  • 17. 1. Frictional losses During flow of fluids frictional forces causes a loss in pressure(Pf pascles) Type of fluid flow also influences the losses i.e either turbulent or viscous. In general pressure drop will be i. Pressure drop 留 velocity of fluid (u) m/s ii. Pressure drop 留 Density of fluid() kg/m3 iii. Pressure drop 留 Length of the pipe (L) m iv. Pressure drop 留/1 diameter of the pipe (D) These relationships are proposed in Fanning equation for Fanning equation: Pf = 2 f2uL / D (viscous/turbulent) f = frictional factor Pf = Pressure drop , Pa Equ considers the friction losses when fluid is passing through straight pipe Value of f depends on: Nature of flow of fluid ( viscous/turbulent) Roughness of inner surface of pipe. For viscous flow H & P equ is employed for calculating pressure drop Hagen Poiseullie equation = 32 Lu侶 / D2 (Viscous flow) Friction losses are permanent , so potential & kinetic energies are converted into heat
  • 18. Losses in fitting large number of fittings are introduced in pipe during the flow of fluid for long distances. This leads to disturbance in the flow and hence loss of energy. These losses may be either due to change in the direction of flow or change in the of fitting like union couplings or even some valve and meters. Losses in the fittings are expressed in terms of an equivalent length of straight pipe (ELSP) which is in forms of a number as per the diameter of pipe. These numbers are used to convert the fitting in to its equivalent of straight pipe Equivalent length of fitting = ELSP * internal diameter of pipe
  • 19. Fanning equation is applicable for the losses in straight pipe. When fitting are introduced into a straight pipe, they cause disturbance in the flow, which result in the additional loss of energy losses in fitting may be due to 1. Change in direction e.g elbow fitting 2. Change in the type of fittings e.g. coupling, union, valve fitting etc Tee fitting Equivalent length = 90 Globe valve equivalent length = 300 Equivalent fitting = Equivalent fitting x internal diameter For globe valve= 300 x 50 = 15 meter That means globe valve is equal to 15 meters straight line, so this length is substituted in fanning equation= 300 x 50 = 15 meter
  • 20. Enlargement loss If the cross section of the pipe enlarges gradually, the fluid adapts itself to the changed section without any disturbance, So no loss of energy If the cross section of the pipe changes suddenly then loss in energy is observed due to eddies. These are greater at this point than straight line pipe Then u2< u1 For sudden enlargement = He = (u1 u2)2 / 2g He= loss of head due to sudden enlargement
  • 22. Manometers Manometers are the devices used for measuring the pressure difference Manometers are used to measure the pressure of any fluid Different type of manometers are there they are 1. Simple manometer 2. Differential manometer 3. Inclined manometer 1. Simple manometer This manometer is the most commonly used one It consists of a glass U shaped tube filled with a liquid A- of density A kg /meter3 and above A the arms are filled with liquid B of density B The liquid A and B are immiscible and the interference can be seen clearly If two different pressures are applied on the two arms the meniscus of the one liquid will be higher than the other Let pressure at point 1 will be P1 Pascal's and point 5 will be P2 Pascal's The pressure at point 2 can be written as = P1+ (m + R ) B g As (m + R ) = distance from 3 to 5
  • 23. Since the points 2 and 3 are at same height the pressure at 3 can be written as Pressure at 3 =P1+ (m + R ) B g Pressure at 4 can be written as = P2 + gm B or = P1+ B ( m + R ) g - a R g Both the equations should be equal P2 + gm B = P1+ B ( m + R ) g- A R g P1 P2 = gm B - B ( m + R) g + A R g P = gm B - gm B - R B g + R A =R ( A- B )g Pressure difference can be determined by measuring R Manometers are use in measuring flow of fluid
  • 24. 2. Differential manometers These manometers are suitable for measurement of small pressure differences It is also known as two Fluid U- tube manometer It contains two immiscible liquids A and B having nearly same densities The U tube contains of enlarged chambers on both limbs Using the principle of simple manometer the pressure differences can be written as P =P1 P2 =R (C A) g Hence smaller the difference between C and A larger will be R
  • 25. 3. Inclined tube manometers Many applications require accurate measurement of low pressure such as drafts and very low differentials, primarily in air and gas installations. In these applications the manometer is arranged with the indicating tube inclined, as in Figure, therefore providing an expanded scale. i.e. In this type of manometer the leg containing one meniscus must move a considerable distance along the tube. This enables the measurement of small pressure changes with increased accuracy. P1 P2 = g R ( A - B) sin 留 For measuring small difference in pressure this type of manometer is used.
  • 26. Measurement of rate of flow of fluids Whenever fluid are used in a process it is necessary to measure the rate at which the fluid is flowing through the pipe Methods of measurement are 1. Direct weighing or measuring 2. Hydrodynamic methods Orifice meter Venturi meter Pitot meter Rotameter 3. Direct displacement meter 1. Direct weighing or measuring The liquid flowing through a pipe is collected for specific period at any point and weighed or measured, and the rate of flow can be determined. Gases cannot be determined by this method
  • 27. Orifice meter Principle Orifice meter is a thin plate containing a narrow and sharp aperture When a fluid stream is allowed to pass through a narrow constriction the velocity of the fluid increase compared to up stream This results in decrease in pressure drop and the difference in the pressure may be read from a manometer The velocity of the fluid at thin constriction may be written as U0 =C 0 2g H H = can be measured by manometer C0 = constant U0 = velocity of fluid at the point of orifice meter Applications Velocity at either of the point A and B can be measured Volume of liquid flowing per hour can be determined by knowing the area of the cross section
  • 28. Construction It is considered a thin plate containing a sharp aperture through which fluid flows Normally it is placed between long straight pipes For present discussion plate is introduced into pipe and manometer is connected at points A and B Working Orifice meter is referred as the variable head meter, i.e it measure the variation in the pressure across a fixed point construction placed in the path of flow When fluid is allowed to pass through the orifice the velocity of the fluid at point B increase, as a result at point A pressure will be increased. Difference in the pressure is measured by manometer Bernoulli's equation is applied to point A and point B for experimental conditions U02 UA2 =C02g. H U0 = velocity of fluid at orifice UA = velocity of fluid at point A C0 = constant If the diameter of the orifice is 1/5 or less of the pipe diameter then UA is neglected
  • 31. When fluid is allowed to pass through narrow venturi throat then velocity of fluid increases and pressure decreases Difference in upstream and downstream pressure head can be measured by using Manometer
  • 32. Advantage Power loss is less Head loss is negligible Disadvantage Expensive Not flexible it is permanent Need technical export Differentness between or Why Venturi meter if Orifice meter is available? Main disadvantage of orifice meter is power loss due to sudden contraction with consequent eddies on other side of orifice plate We can minimize power loss by gradual contraction of pipe Ventury meter consist of two tapperd (conical section) inserted in pipeline Friction losses and eddies can be minimized by this arrangement ifice and venture meter
  • 34. Pitot Tube Principle: Pitot tube consists of sensing element with a small constriction compared to the size of the flow channel. When the sensing element is inserted at the center of the stream, the velocity of flow is increased. This results in decrease in pressure head. Hp = u2 2g 40
  • 35. Tube are inserted in the flow shown is the figure U2 = Cv 2g. H Cv = Coefficient of Pitot tube Working of Pitot Tube A pitot tube is simply a small cylinder that faces a fluid so that the fluid can enter it Because the cylinder is open on one side and enclosed on the other, fluid entering it cannot flow any further and comes to a rest inside of the device A diaphragm inside of the pitot tube separates the incoming pressure (static pressure) from the stagnation pressure (total pressure) of a system The difference between these two measurements determines the fluids rate of flow
  • 36. Advantages: Pitot tubes measure pressure levels in a fluid They do not contain any moving parts and routine use does not easily damage them Also, pitot tubes are small and can be used in tight spaces that other devices cannot fit into Disadvantages: Foreign material in a fluid can easily clog pitot tubes and disrupt normal readings as a result This is a major problem that has already caused several aircraft to crash and many more to make emergency landings
  • 37.
  • 39. Float: Floats may be constructed of metals of various densities from lead to aluminum or from glass or plastic. Stainless-steel floats are common ones Float shapes and proportions are also varied for different applications For small flows floats are spherical in shape Working As the flow is upward through the tapered tube the plummet rises and falls depend on the flow rate Greater the flow rate higher the rise of float Fluid enters the tapered tube, some of the fluid strikes directly the float. Some of the fluid passes from sides Two forces are acting in this case: Upthurst Force (Buoyancy) Weight of the float When equilibrium is established the float comes to rest
  • 40. Measurement of flow rate The flowrate is measured directly from calibrated scale. The reading is noted generally from ending point of cap of the float. Advantages: No external power or fuel Manufactured of cheap materials Since the area of the flow passage increases as the float moves up the tube, the scale is approximately linear. Disadvantages: Accuracy of rotameter Uncertainty of the measurement Impact of gravity Rotameter is a device used to measure fluid flow, in which a float rises in a tapered vertical tube to a height dependent on the rate of flow through the tube
  • 41. QUE BANK Define fluids with its properties Differentiate between fluid statics and fluid dynamics Recall the applications of Reynolds number Discuss the types of energy losses Describe the construction and working of simple monometer Compare and contrast between the three types of monometers Point out the devices used for measuring the rate of flow of fluids Explain the principle and working of orifice meter Discuss the construction and working of venturi meter Differentiate between orifice and venturi meter Justify the importance of pitot tube Recall the importance of rotameter as a fluid flow measuring device