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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