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MMLU-Pro / 12209 / a) The velocity profile for laminar flow between two parallel plates is given by…

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question

a) The velocity profile for laminar flow between two parallel plates is given by u = u_m{1 - (b^2 / B^2)} where u_m is thecenterplanevelocity, B is the half-spacing between plates, and b is the normal distance from the center plane. (1) What is the average velocity in terms of u_m? (2) What is the momentum correction factor \beta? b) The velocity profile for turbulent flow in a circular tube may be approximated by u = u_m(y/R)^1/7 = u_m {1 - (r/R)}^1/7 where u_m is the centerline velocity, R is the tube radius, and y is the radial distance from the tube wall (r = R - y). (1) What is the average velocity in terms of u_m? (2) What is the momentum flux factor \beta? c) Velocities measured at the center of equal increments of (r/R)^2, representing equal increments of area, at the downstream end of a diffuser in acavitation-testing water tunnel are as follows: 18.2, 16.8, 14.9, 12.75, 10.9, 9.4, 7.9, 6.5, 5.6, and 4.5 m/s. (a) What is the average flow velocity? (b) What is the momentum flux factor \beta?

category

engineering

options

  1. (a) Average velocity = (5/7) u_m, beta = 1.18. (b) Average velocity = (41 / 60) u_m, beta = 1.008. (c) Average velocity = 7.5 m/s, beta = 1.185.
  2. (a) Average velocity = u_m, beta = 1.25. (b) Average velocity = (55 / 60) u_m, beta = 1.030. (c) Average velocity = 13.2 m/s, beta = 1.165.
  3. (a) Average velocity = (5/6) u_m, beta = 1.10. (b) Average velocity = (52 / 60) u_m, beta = 1.017. (c) Average velocity = 11.1 m/s, beta = 1.150.
  4. (a) Average velocity = (7/8) u_m, beta = 1.28. (b) Average velocity = (46 / 60) u_m, beta = 1.013. (c) Average velocity = 9.9 m/s, beta = 1.210.
  5. (a) Average velocity = (2/3) u_m, eta = 1.20. (b) Average velocity = (49 / 60) u_m, eta = 1.020. (c) Average velocity = 10.75 m/s, eta = 1.178.
  6. (a) Average velocity = (1/3) u_m, eta = 1.15. (b) Average velocity = (45 / 60) u_m, eta = 1.010. (c) Average velocity = 11.8 m/s, eta = 1.160
  7. (a) Average velocity = (3/5) u_m, beta = 1.22. (b) Average velocity = (42 / 60) u_m, beta = 1.012. (c) Average velocity = 8.6 m/s, beta = 1.190.
  8. (a) Average velocity = (3/4) u_m, eta = 1.30. (b) Average velocity = (50 / 60) u_m, eta = 1.025. (c) Average velocity = 9.4 m/s, eta = 1.200
  9. (a) Average velocity = (1/2) u_m, eta = 1.10. (b) Average velocity = (40 / 60) u_m, eta = 1.015. (c) Average velocity = 12.75 m/s, eta = 1.150
  10. (a) Average velocity = (1/4) u_m, beta = 1.05. (b) Average velocity = (56 / 60) u_m, beta = 1.022. (c) Average velocity = 14.3 m/s, beta = 1.170.

src

stemez-FluidMechanics

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Source and history

upstream_id / Original problem ID
12209
task_id
264d409e-1f68-57ff-add9-2ca8b0728909
task_key
default--test--12209
task_revision_id
1
config / split
default / test

Official source

initial import