Fluid Mechanics GATE

(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 Uo The velocity profile at the inlet a-b is uniform, while that at a downstream location c-d is given by

$u=U_o\left [ 2\left ( \frac{y}{\delta } \right )-\left ( \frac{y}{\delta} \right )^2 \right ]$

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 ___________

[GATE 16 S1, 2 marks]

Question #2

Air ($\rho$ = 1.2 kg/m3and kinematic viscosity,$\nu$ = 2 × 10−5 m2/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 _______

[GATE 15 S1, 2 marks]

Question #3

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]

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 _______

[GATE 14 S2, 2 marks]

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