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Question

The velocity profile of a fluid over a flat plate is parabolic in nature. At a distance of 15 cm from the plate, the velocity of fluid is maximum i.e 100 cm/s. Calculate the shear stress at a distance of 10 cm from the plate if the viscosity of the fluid is 10 poise.


A
4.53 N/m2
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B
2.26 N/m2
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C
2.35 N/m2
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D
None of these
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Solution

The correct option is A 4.53 N/m2
Viscosity of fluid (μ)=1010=1 Ns/m2
The velocity profile given is parabolic, so the equation of velocity profile will be
u=ay2+by+c
where a,b and c are constants.
The values of a,b and c will be determined from the following boundary conditions.
(a) at y=0; u=0
(b) at y=15 cm; u=100 cm/s
(c) at y=15 cm; dudy=0
From (a), we get c=0
From (b)
100=a(15)2+b(15) ..........(1)
From (c)
dudy=2ay+b
2a(15)+b=0..............(2)
Solving Eq.(1) and (2), we get
a=0.44 and b=13.33
So velocity profile become
u=0.44y2+13.33y
From formula,
shear stress (τ)=μ(dudy)
At y=10 cm,
τ=μ(dudy)y=10=1×(13.332×0.44×10)=4.53 N/m2
Hence, option (a) is the correct answer.

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