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W2 Example 6 Answers

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The document provides calculations to determine water density at station A (A), the latitude corresponding to a given Coriolis parameter, and the latitude at which two ocean stations with different water densities and depths are located. It rearranges geostrophic flow and Coriolis parameter equations to solve for the desired variables, and substitutes known values from the questions to calculate numerical solutions.

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6a The geostrophic flow between two stations A and B is 0.12ms-1. The stations are 150km apart and the water at station B is 1026.7kgm-3 and is 500m above a reference point. If the Coriolis parameter is 1.031 x 10-4s-1, what is the density of the water at station A?
6a Rearrange the equation to make A the subject:
6a Rearrange the equation to make A the subject: vg = gh fL A B A
6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A
6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B
6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B A fLvg gh A = B
6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B A fLvg gh A = B A fLvg gh 1 = B
6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B A fLvg gh A = B A fLvg gh 1 = B A = B fLvg gh 1
6a Substitute in the values you know:
6a Substitute in the values you know: A = 1026.7 1.031 x 104 x 150,000 x 0.12 9.81 x 500 1 = . ろ
6a Substitute in the values you know: A = 1026.7 1.031 x 104 x 150,000 x 0.12 9.81 x 500 1 = . ろ Replace the values for their units, combine like units and cancel them:
6a Substitute in the values you know: A = 1026.7 1.031 x 104 x 150,000 x 0.12 9.81 x 500 1 = . ろ Replace the values for their units, combine like units and cancel them: kgm3 s1. m. ms1 ms2. m 1 = kgm3 m2s2 m2s2 1 = ろ
6b At what latitude is the Coriolis parameter equal to 4.97 x 10-5s-1?
6b Substitute the values you know into the Coriolis equation:
6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin
6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin Rearrange for latitude:
6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin Rearrange for latitude: 4.97 x 105 2 x 7.27 x 105 = sin
6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin Rearrange for latitude: 4.97 x 105 2 x 7.27 x 105 = sin sin 1 4.97 x 105 2 x 7.27 x 105 = = . 属
6c Point A in the Atlantic Ocean is at 42.5属W and has a water density of 1027.1kgm-3. Point B is at 43.3属W, has a water density 1026.5kgm-3 and sits 1000m above a reference isobar. If the geostrophic flow associated with this slope is 0.9ms- 1, at what latitude do these points sit? They are both at the same latitude at which 1 degree of longitude is equivalent to roughly 85km.
6c Rearrange the geostrophic flow equation for f:
6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A
6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A Substitute the Coriolis equation for f and rearrange for :
6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A Substitute the Coriolis equation for f and rearrange for : 2立 sin = gh vgL A B A
6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A Substitute the Coriolis equation for f and rearrange for : 2立 sin = gh vgL A B A = sin1 gh vgL A B A 2立
6c Work out the distance between stations by converting between degrees of longitude and metres:
6c Work out the distance between stations by converting between degrees of longitude and metres: distance m = 85,000 x 43.3 42.5 = 68,000m
6c Work out the distance between stations by converting between degrees of longitude and metres: distance m = 85,000 x 43.3 42.5 = 68,000m Substitute values into the equation for :
6c Work out the distance between stations by converting between degrees of longitude and metres: distance m = 85,000 x 43.3 42.5 = 68,000m Substitute values into the equation for : = sin1 9.81 x 1000 0.9 x 68,000 1027.1 1026.5 1027.1 2 x 7.27 x 105 = . 属

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W2 Example 6 Answers

  • 1. 6a The geostrophic flow between two stations A and B is 0.12ms-1. The stations are 150km apart and the water at station B is 1026.7kgm-3 and is 500m above a reference point. If the Coriolis parameter is 1.031 x 10-4s-1, what is the density of the water at station A?
  • 2. 6a Rearrange the equation to make A the subject:
  • 3. 6a Rearrange the equation to make A the subject: vg = gh fL A B A
  • 4. 6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A
  • 5. 6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B
  • 6. 6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B A fLvg gh A = B
  • 7. 6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B A fLvg gh A = B A fLvg gh 1 = B
  • 8. 6a Rearrange the equation to make A the subject: vg = gh fL A B A fLvg gh = A B A A fLvg gh = A B A fLvg gh A = B A fLvg gh 1 = B A = B fLvg gh 1
  • 9. 6a Substitute in the values you know:
  • 10. 6a Substitute in the values you know: A = 1026.7 1.031 x 104 x 150,000 x 0.12 9.81 x 500 1 = . ろ
  • 11. 6a Substitute in the values you know: A = 1026.7 1.031 x 104 x 150,000 x 0.12 9.81 x 500 1 = . ろ Replace the values for their units, combine like units and cancel them:
  • 12. 6a Substitute in the values you know: A = 1026.7 1.031 x 104 x 150,000 x 0.12 9.81 x 500 1 = . ろ Replace the values for their units, combine like units and cancel them: kgm3 s1. m. ms1 ms2. m 1 = kgm3 m2s2 m2s2 1 = ろ
  • 13. 6b At what latitude is the Coriolis parameter equal to 4.97 x 10-5s-1?
  • 14. 6b Substitute the values you know into the Coriolis equation:
  • 15. 6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin
  • 16. 6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin Rearrange for latitude:
  • 17. 6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin Rearrange for latitude: 4.97 x 105 2 x 7.27 x 105 = sin
  • 18. 6b Substitute the values you know into the Coriolis equation: 4.97 x 105 = 2 x 7.27 x 105 x sin Rearrange for latitude: 4.97 x 105 2 x 7.27 x 105 = sin sin 1 4.97 x 105 2 x 7.27 x 105 = = . 属
  • 19. 6c Point A in the Atlantic Ocean is at 42.5属W and has a water density of 1027.1kgm-3. Point B is at 43.3属W, has a water density 1026.5kgm-3 and sits 1000m above a reference isobar. If the geostrophic flow associated with this slope is 0.9ms- 1, at what latitude do these points sit? They are both at the same latitude at which 1 degree of longitude is equivalent to roughly 85km.
  • 20. 6c Rearrange the geostrophic flow equation for f:
  • 21. 6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A
  • 22. 6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A Substitute the Coriolis equation for f and rearrange for :
  • 23. 6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A Substitute the Coriolis equation for f and rearrange for : 2立 sin = gh vgL A B A
  • 24. 6c Rearrange the geostrophic flow equation for f: f = gh vgL A B A Substitute the Coriolis equation for f and rearrange for : 2立 sin = gh vgL A B A = sin1 gh vgL A B A 2立
  • 25. 6c Work out the distance between stations by converting between degrees of longitude and metres:
  • 26. 6c Work out the distance between stations by converting between degrees of longitude and metres: distance m = 85,000 x 43.3 42.5 = 68,000m
  • 27. 6c Work out the distance between stations by converting between degrees of longitude and metres: distance m = 85,000 x 43.3 42.5 = 68,000m Substitute values into the equation for :
  • 28. 6c Work out the distance between stations by converting between degrees of longitude and metres: distance m = 85,000 x 43.3 42.5 = 68,000m Substitute values into the equation for : = sin1 9.81 x 1000 0.9 x 68,000 1027.1 1026.5 1027.1 2 x 7.27 x 105 = . 属