(a)
The characteristic scale for v, y-component of velocity.
Answer to Problem 27P
The characteristic scale for v, y-component of velocity is
Explanation of Solution
First, we need to use continuity equation for velocity component.
From continuity equation,
We have,
Now, to obtain order of magnitude. We need to use characteristic scale separately.
We have,
Now, characteristic scale v is,
(b)
The order of magnitude of inertial term to that of viscous and pressure term.
Answer to Problem 27P
The characteristic scale for v, y-component of velocity is
Explanation of Solution
First, we need to use momentum of x-component.
As we know that the flow is carried out in two-dimensional, so the z component will be zero.
Now, to obtain order of magnitude. We need to use characteristic scale separately.
We have,
Now,
The second term of viscosity is very smaller as compared to the second viscous term. So, we neglect this term (ho<
Now, we need to multiply all the order of magnitude with a factor of
Now,
We can see that the order of magnitude consists a factor of
(c)
If the value of Reynolds number is less than 1 and (ho<
Explanation of Solution
First, we need to use momentum of x-component.
As we know that the flow is carried out in two-dimensional, so the z component will be zero.
Now, to obtain order of magnitude. We need to use characteristic scale separately.
We have,
Now,
The second term of viscosity is very smaller as compared to the second viscous term. So, we neglect this term. (ho<
Now,
We can see that the order of magnitude consists a factor of
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Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
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