Fluid Dynamics A small low-speed wind tunnel is being designed for calibration o

Question

Fluid Dynamics

A small low-speed wind tunnel is being designed for calibration of hot wires. The air is at 19 degree C. The test section of the wind tunnel is 30 cm in diameter and 30 cm in length. The flow through the test section must be as uniform as possible. The wind tunnel speed ranges from 1 to 8 m/s, and the design is to be optimized for an air speed of V = 4.0 m/s through the test section. For the case of nearly uniform flow at 4.0 m/s at the test inlet section, by how much will the centerline air speed accelerate by the end of the test section? Recommend a design that will lead to a more uniform test section flow.

Explanation / Answer

GIVEN:- T = 19C, D = 30cm, L = 30cm, V = 4m/s

TO FIND:- (1) Percentage of velocity increase by the end of test section = ?, (2) Design recommendation.

SOLUTION:-

Assuming steady, incompressible and laminar flow. Kinematic viscosity of air v = 1.507 x 10^-5 m2/s

(1) Reynold's number at the end of section Re = V x L / v = 4 x 0.30 / 1.507 x 10^-5 = 7.96 x 10^4

Displacement thickness at the end of test section = d = (1.72 x L) / Re^0.5 = (1.72 x 0.30) / (7.96 x 10^4) ^0.5

d = 1.83mm

By conservation of mass relation---

Vout x Aout = Vin x Ain i.e. Vout = Vin x 3.142(D/2)^2 / 3.142(D/2 - d)^2

i.e. Vout = 4 x 3.142(0.30/2)^2 / 3.142(0.30/2 - 1.83)^2 = 4.10 m/s

Therefore % of velocity increase = (4.10 - 4) / 4 x 100 = 2.5 % (ANSWER)

(2) Recommended design - To increase the exit diameter at the end of the test section by 1.83 mm (ANSWER)

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