Question

The free-stream velocity in the test section during an early morning wind tunnel test was 100 kph and the temperature was 280 k (use rho = 1.2 kg/m3, μ = 1.8 10−5 ns/m2). the same test is repeated in the afternoon but now the temperature is 310 k (to calculate rho, use the ideal gas relation, μ = 2.0*10−5 ns/m2). a. calculate the desirable free-stream speed in order to maintain the morning’s reynolds number. b. at what speed will the forces (e.g. lift and drag) be the same as in the morning?

Answer 1

To maintain the same Reynolds number when temperature and air density change, we solve for the appropriate free-stream speed using the Reynolds number formula.

Step-by-step explanation:

To maintain the same Reynolds number for different temperatures and densities in a wind tunnel, we use the Reynolds number formula: Re = rho * V * L / mu, where rho is the density, V is the velocity, L is the characteristic length, and mu is the dynamic viscosity. Since we want to maintain the Reynolds number and the characteristic length isn't changing, we can solve for the desirable free-stream speed to maintain the morning's Reynolds number in the afternoon when the temperature and thus the air density changes.

To answer part A, first calculate the Reynolds number from the morning session. From the ideal gas law, rho = P / (R * T), where P is pressure, R is the specific gas constant for air, and T is temperature. Use this to find the new density in the afternoon and solve for the new velocity to maintain the same Reynolds number. For part B, the speed will remain the same as in (A) because lift and drag are proportional to the square of the velocity and any change in air density is accounted for by the speed change to keep Reynolds number constant.