GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 27 of 65

Marks: +1, -0

A flat plate of width

L=1 {m}

is pushed down with a velocity

U=0.01 {m} {/} {s}

towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity,

U_{\text "avg "}

of the fluid (in

{m} {/} {s}

) draining out at the instant shows in the figure is________ (correct to three decimal places).

Your Answer:

Validate

Solution:

Assuming length of plate as

{B}

Let in infinitely small time 'dt' the plate is displaced with 'dh'
So,

\;\; \;{d h}/{d t}=U

As per continuity,
Rate of mass displaced through plate= Rate of mass displaced between plates and wall

L B d h=2 × U_{\;\text "avg "\;} × d × B d t

L \;{d h}/{d t}=2 U_{ {avg}} d

U_{\;\text "awg "\;}=\;{L U}/{2 d}=\;{1 × 0.01}/{2 × 0.1}=0.05 {m} {/} {s}

A_{1} U_{1}=A_{2} u_{\;\text "avg "\;}

L × B × U=2 × d × B × u_{\;\text "avg "\;}

Since the flow is

2 {D}

the velocity of flow in direction perpendicular to plane of paper is zero.

1 × 0.01=2 × 0.1 × u_{\;\text "avg "\;}

u_{\;\text "avg "\;}=0.05 {m} {/} {sec}

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