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need help with 2.1 and 2.2.:Non-dimentionalization and Analytical Solution

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need help with 2.1 and 2.2.:Non-dimentionalization and Analytical Solution
Answered Same Day Dec 26, 2021

Solution

David answered on Dec 26 2021
127 Votes
Ans. 1
For the given fluid flow problem,
The height of the flow, h
The simplified Nervier-Stokes principle,


  



2
2
0
(0) 0
( )
dp u
dx y
u
u h U

Here, u is velocity of fluid,  is viscosity, and p is the fluid pressure,
The flow of the fluid where the plate is moving and the bottom plate is fixed,




Hence the upper plate is moving with the velocity and the lower plate is fixed, the
pressure gradient across the flow will be negative and the magnitude,
dp
dx
 and it is
maintaining along with its flow direction,
According to the Navies-Stokes principle,
2
2
0
u dp
const
y...
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