Chapter 7, Problem 1CP

What is the difference between the upstream velocity and the free-stream velocity? For what types of flow are these two velocities equal to each other?

To determine

Difference between"Upstream flow velocity" and "free stream velocity"and for which flow are they equal.

Answer to Problem 1CP

Upstream velocity represents approaching velocity while free stream velocity represents velocity of fluid relative to the immersed body(solid).

They are equal in uniform flow.

The difference between upstream flow velocity and free stream velocity is given in table below:

Upstream flow velocity	Free stream velocity
The velocity(V) at which any fluid flow approaches an immersed body is known as upstream flow velocity.	The sufficiently far away velocity of the fluid which is relative to the immersed body(solid) is the free stream velocity. It is denoted by $u_{\infty }$.
It is the actual velocity of fluid flowing just before approaching the immersed body	It is the velocity which exists at end of the velocity boundary layer around the immersed body.

"Upstream flow velocity " and "free stream velocity" are same/equal when:

a. There is uniform fluid flow.

b. When the immersed body in fluid is relatively in comparison to uniform fluid flow rate, where it is immersed.

Explanation of Solution

The difference between upstream flow velocity and free stream velocity is given in table below:

Upstream flow velocity	Free stream velocity
The velocity(V) at which any fluid flow approaches an immersed body is known as upstream flow velocity.	The sufficiently far away velocity of the fluid which is relative to the immersed body(solid) is the free stream velocity. It is denoted by $u_{\infty }$.
It is the actual velocity of fluid flowing just before approaching the immersed body	It is the velocity which exists at end of the velocity boundary layer around the immersed body.

"Upstream flow velocity " and "free stream velocity" are same/equal when:

a. There is uniform fluid flow.

b. When the immersed body in fluid is relatively in comparison to uniform fluid flow rate, where it is immersed.