(Detailed Solution)GATE ME Question on Boundary layer therory(Fluid Mechanics)

Question #1

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is U_{o} The velocity profile at the inlet a-b is uniform, while that at a downstream location c-d is given by

The ratio of the mass flow rate, $\dot{m_{bd}}$ , leaving through the horizontal section b-d to that entering through the vertical section a-b is ___________

Air ($\rho$ = 1.2 kg/m3and kinematic viscosity,$\nu$ = 2 × 10^{−5} m^{2}/s) with a velocity of 2 m/s flows over the top surface of a flat plate of length 2.5 m. If the average value of friction coefficient is $C_f=\frac{1.328}{\sqrt{Re_x}}$, the total drag force (in N) per unit width of the plate is _______

Within a boundary layer for a steady incompressible flow, the Bernoulli equation
(A) holds because the flow is steady
(B) holds because the flow is incompressible
(C) holds because the flow is transitional
(D) does not hold because the flow is frictional

[GATE 15 S2, 1 mark]

Solution

Answer:(D)

Bernoulli’s equation is applicable only to non viscous flow. The flow inside the boudary layer is viscous.Hence we cannot appy bernoulli’s equation inside boundry layer region.

Question #4

Consider laminar flow of water over a flat plate of length 1 m. If the boundary
layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is _______

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