How do I find the pressure coefficient at the stagnation point?

[gharrington44]

a. A very large reservoir of pressurized air feeds a contraction and forms a free jet of air of circular cross section and diameter 60 cm in a laboratory, where the ambient pressure is atmospheric. A Pitot static tube is arranged in the jet and attached to a vertical U-tube manometer containing alcohol. If the difference in levels recorded by the manometer is 65 mm, find the air speed.

I was able to find the air speed leading the contraction to be 28.8 m/s

b. The Pitot static tube is removed and replaced by a small body, which is equipped with static pressure holes in its surface. If the minimum gauge pressure recorded on the body is found to be -310 Pa, find the maximum velocity on the body.

I found the maximum velocity of the body to be 36.5 m/s.

c. State the values of pressure coefficient on the body (i) at the stagnation point, and (ii) at a point where the velocity achieves a value 50% above the value in the jet.

I have no idea how to approach this at all. I am assuming the stagnation point is in the center of the object where the air velocity is 0. But I am not familiar with a pressure coefficient or where to find where the velocity is half of what it should be.

 

[mark726]

Thank you for your post. I can provide some insights and explanations for your questions.

For part c, the pressure coefficient is a dimensionless quantity that relates the local pressure at a point on an object to the free stream pressure. It is defined as Cp = (P-Pinf)/0.5*rho*Vinf^2, where P is the local pressure, Pinf is the free stream pressure, rho is the air density, and Vinf is the free stream velocity. The pressure coefficient is used to characterize the aerodynamic forces on an object and is often represented graphically as a pressure distribution along the surface of the object.

(i) At the stagnation point, the velocity is zero, so the pressure coefficient can be calculated as Cp = (P-Pinf)/0.5*rho*Vinf^2 = (P-Pinf)/0, where P is the local pressure and Pinf is the free stream pressure. Since the velocity is zero, the pressure coefficient at the stagnation point is infinite.

(ii) To find the point where the velocity is 50% above the value in the jet, we need to first determine the velocity in the jet. From part a, we know that the air speed in the jet is 28.8 m/s. So, the velocity we are looking for is 50% above this, which is 43.2 m/s. Using this velocity, we can calculate the pressure coefficient at this point using the same formula as before. The only difference is that now the velocity is 43.2 m/s instead of 28.8 m/s. So, the pressure coefficient at this point would be Cp = (P-Pinf)/0.5*rho*Vinf^2 = (P-Pinf)/(0.5*rho*43.2^2).

I hope this helps to clarify the concept of pressure coefficient and how to calculate it at different points on an object. Please let me know if you have any further questions.