Consider the incompressible flow of fluid in a boundary layer as depicted in Example 4.2. Show that the friction drag force of the fluid on the surface is given by

\[F_{f}=\int_{0}^{\delta} ho u(U-u) w d y\]

Evaluate the drag force for the conditions of Example 4.2.

Data From Example 4.2

Transcribed Image Text:

Example 4.2 MASS FLOW RATE IN BOUNDARY LAYER The fluid in direct contact with a stationary solid boundary has zero velocity; there is no slip at the boundary. Thus the flow over a flat plate adheres to the plate surface and forms a boundary layer, as depicted below. The flow ahead of the plate is uniform with velocity V=Ui; U=30 m/s. The velocity distribution within the boundary layer (0y6) along ed is approximated as u/U = 2(y/6)-(y/8). The boundary-layer thickness at location d is 6=5 mm. The fluid is air with density p= 1.24 kg/m. Assuming the plate width perpendicular to the paper to be w=0.6 m, calculate the mass flow rate across surface be of control volume abcd. Given: Steady, incompressible flow over a flat plate, p= 1.24 kg/m. Width of plate, w = 0.6 m Velocity ahead of plate is uniform: V = Ui, U = 30 m/s. Atx=xd: Edge of boundary layer d 8=5 mm -20-0 2