GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 58 of 65

Marks: +1, -0

Consider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocity of

1 {cm} {/} {s}

in the

x

-direction. The distance between the plates is

5 {mm}

and the dynamic viscosity of the fluid is

0.01 {N}- {s} {/} {mIf}

the shear stress on the lower plate is zero, the pressure gradient,

\;{∂p}/{∂x}

, (in

{N} {/} {m}^{2}

per

{m}

, round off to 1 decimal place) is

Your Answer:

Validate

Solution:

Given data ;
Velocity of plate,

{V}=1 {cm} {/} {sec}

Distance between the late

=5 {mm}

Dynamic viscosity of fluid

=0.01 {N}- {S} {/} {m}^{2}

Shear stress at lower plate

=0

Pressure gradient

\;{∂ P}/{∂ x}=?

We know that, in case of couette flow, shear stress (

τ

) is given by

τ=\;{µ N}/{B}+(-\;{∂ P}/{∂ x})(\;{B}/{2}-y)

At lower plate,

{y}=0 ; τ=0[

Given

]

0=s \;{0.01 × 0.01}/{0.005}-(\;{∂ P}/{∂ x})[\;{0.005}/{2}-0]

\;{∂ P}/{∂ x}=8 {N} {/} {m}^{2}

per

{m}

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