Question

In a lab experiment for a flat plate zero-pressure gradient boundary layer it is desired to find the friction coefficient (Cf) at location x=1 m from the leading edge of the plate. In order to do this, the momentum thickness of the boundary layer is measured at two locations 0.005m on either side of x=1m. the momentum thickness is measured to be 1.638 mm at x=0.995m and 1.652mm at x=1.005m, respectively, when the approach or free-stream velocity is 5m/s.

a) using the momentum integral theory, find the friction coefficient.

b) what is the predominant state(laminar or turbulent) of the boundary layer at this location if the fluid is a water.show

does the value obtained from the above analysis in (a) agree with know Cf>

what is the friction drag force on the plate

Answer 1

a)

Skin friction coefficient

We have slope

Thus

b)

For water, kinematic viscosity = 1*10^-6 m²/s

Reynolds number at x = 1 m will be Re = VL / = 5 * 1 / (1*10^-6) = 5*10⁶

Since Re > critical value of 5*10⁵, boundary layer is turbulent.

For turbulent flow over flat plate,

C_f = 0.027 / (5*10⁶)^1/7

C_f = 0.00298

This value is quite close to the value found in part a which was 0.0028.

Drag coefficient C_D = (7/6) C_f

= (7/6) * 0.00298

= 0.003477

Drag force D = Cd * 1/2 * rho * V² * A

= 0.003477 * 1/2 * 1000 * 5² * (1*1)

= 43.47 N