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MMLU-Pro / 11874 / Air of density …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Air of density \rho = 0.07 lb/ft^3 and viscosity \mu = 12.9 × 10^-6 lb/ft.sec is flowing through a pipe of 10 in. inside diameter. The mean velocity of the air is 50 ft/sec. Find the velocity at points 0.4 in and 3 in. from the wall. Also find the thickness of the laminar sub-layer if this extends up to u^+ = y^+ = 5. u^+ and y^+ are dimensionless quantities defined as (uy / u\textasteriskcentered) and [(y\rhou\textasteriskcentered) / \mu] respectively, where y is the distance from the surface.

category

engineering

options

  1. Velocity at 0.4 in. from the wall: 45 ft/sec, Velocity at 3 in. from the wall: 55 ft/sec, Thickness of the laminar sub-layer: 0.007 in.
  2. Velocity at 0.4 in. from the wall: 48 ft/sec, Velocity at 3 in. from the wall: 57 ft/sec, Thickness of the laminar sub-layer: 0.006 in.
  3. Velocity at 0.4 in. from the wall: 43 ft/sec, Velocity at 3 in. from the wall: 53 ft/sec, Thickness of the laminar sub-layer: 0.011 in.
  4. Velocity at 0.4 in. from the wall: 51 ft/sec, Velocity at 3 in. from the wall: 61 ft/sec, Thickness of the laminar sub-layer: 0.007 in.
  5. Velocity at 0.4 in. from the wall: 52 ft/sec, Velocity at 3 in. from the wall: 62 ft/sec, Thickness of the laminar sub-layer: 0.009 in.
  6. Velocity at 0.4 in. from the wall: 46 ft/sec, Velocity at 3 in. from the wall: 56 ft/sec, Thickness of the laminar sub-layer: 0.012 in.
  7. Velocity at 0.4 in. from the wall: 55 ft/sec, Velocity at 3 in. from the wall: 65 ft/sec, Thickness of the laminar sub-layer: 0.008 in.
  8. Velocity at 0.4 in. from the wall: 49.5 ft/sec, Velocity at 3 in. from the wall: 59.5 ft/sec, Thickness of the laminar sub-layer: 0.004 in.
  9. Velocity at 0.4 in. from the wall: 47.42 ft/sec, Velocity at 3 in. from the wall: 58.25 ft/sec, Thickness of the laminar sub-layer: 0.005 in.
  10. Velocity at 0.4 in. from the wall: 50 ft/sec, Velocity at 3 in. from the wall: 60 ft/sec, Thickness of the laminar sub-layer: 0.01 in.

src

stemez-TransportPhenomena

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Source and history

upstream_id / Original problem ID
11874
task_id
bd683eff-0a69-5278-9001-5fb0df3eecda
task_key
default--test--11874
task_revision_id
1
config / split
default / test

Official source

initial import