Find the torque on a bent pipe

[thshen34]

Homework Statement

Consider a steady flow of liquid with a density of 805 kg/m3 through a rotating tube as shown in the sketch. The flow speed is V = 5 m/s. If ω = 10 rad/s, find the torque necessary to rotate the pipe. Assume a uniform velocity distribution at the exit from the pipe, and that the
incoming fluid has no angular momentum.

Homework Equations

Conversation of momentum and Rotational Forces

The Attempt at a Solution

So I calculated the force of the fluid on the pipe, which is ρV(∏D^4)/4, which can be split up to y and x components, by multiplying cosθ and sinθ, respectively. However, this does not create any moment about the axis of rotation. So, my guess is that the x component of the force provides the centripetal force of the ω rotation. Given that F = mv^2/r, I'm thinking that the we can find the torque by Fr = mv^2, since we know v. Now, can someone help me find out what m ought to be? Is it just the mass of the bent pipe portion?

I think this is a valid attempt a solution, I only need a bit of concept cleared up. I hope someone will review this question please.

Thanks,

 

[KataKoniK]

Dear ,

Your approach seems to be on the right track. To find the torque necessary to rotate the pipe, you can use the equation τ = F*r, where F is the force acting on the pipe and r is the distance from the axis of rotation to the point where the force is applied. In this case, the force acting on the pipe is the x component of the force you calculated, which is ρV(∏D^4)/4 * sinθ. The distance r can be calculated using the radius of the pipe and the angle θ.

However, the mass you are looking for is not the mass of the bent pipe portion, but rather the mass of the fluid flowing through the pipe. This can be calculated using the density and the volume flow rate, which can be found by multiplying the cross-sectional area of the pipe by the flow speed. Once you have the mass, you can use it in the equation τ = F*r to find the torque necessary to rotate the pipe.

I hope this helps clarify your approach. Let me know if you have any further questions.