Find the Pressure gradient that would produce a null shear s

Find the Pressure gradient that would produce a null shear stress on the stationary plate where A = 7 and B = 2 and U_m (model velocity) = 1550 km/h.

4. A pressure change of 50+A/10 [kPa] is measured between the surface of a model space shuttle and a given point in the undisturbed air flow. The temperature and pressure in the wind tunnel are 290 [K] and 120 + B/5 [kPal, respectively. Determine the pressure change and speed of the space shuttle prototype working above 12 [km] sea level.

Solution

Pressure Change = 50 + 7 / 10   = 50.7 kPa

P = rho * R * T

120.4 * 10^3 = rho * 287 * 290

rho = 1.4466 kg/m^3

using bernoullis equation

pressure change   = 0.5 * rho * v^2

50.4 * 10^3 = 0.5 * 1.4466 * v^2

v = 263.97 m/s

U_m (model velocity ) = 1550 km/hr or 430.5556 m/s