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Fluid Mechanics: Fundamentals and Applications 2nd Edition

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Chapter: Problem:

A group of students is designing a small, round (axisymmetric), low-speed wind tunnel for their senior design project (Fig. P9-125E). Their design calls for the axial component of velocity to increase linearly in the contraction section from u z 0 to u z L. The air speed through the test section is to be u z L = 120 ft/s. The length of the contraction is L = 3.0 ft, and the entrance and exit diameters of the contraction are D 0 = 5.0 ft and D L = 1.5 ft, respectively. The air is at standard temperature and pressure. ( a) Verify that the flow can be approximated as incompressible. ( b) Generate an expression for the radial velocity component u r between z = 0 and z = L, staying in variable form. You may ignore frictional effects (boundary layers) on the walls. ( c) Generate an expression for the stream function ψ as a function of r and z.( d) Plot some streamlines and design the shape of the contraction, assuming that frictional effects along the walls of the wind tunnel contraction are negligible.

Chapter: Problem:
  • Step 1 of 4


    Usually a gas flow is a compressible flow, but if the density changes are under about 5 percent, which means the Mach number is smaller than 0.3, the gas flow can be seen as incompressible.

    At room temperature and regular pressure, the speed of sound is.

    Calculate the Mach number for the air flow by using the following relation:

    Here, exit velocity of the air is, and speed of the sound is c.

    Substitute for, and for c.

    Therefore, the air flow can be approximated as.

  • Chapter , Problem is solved.
Corresponding Textbook

Fluid Mechanics with Student Resources DVD 2nd edition 9780077295462 0077295463
Fluid Mechanics: Fundamentals and Applications | 2nd Edition
This is an alternate ISBN. View the primary ISBN for: Fluid Mechanics: Fundamentals and Applications 2nd Edition Textbook Solutions