Solved Problem: Force of a Water Jet with a Moving Control Volume

MEC516/BME516 Fluid Mechanics Chapter 3 Control Volume Analysis: This linear momentum problem involves calculating the force and power generated by a fluid jet impinging upon a vane moving at constant velocity. The analysis requires using relative velocity and a control volume that moves with the vane. This is an exam caliber question.
A copy (pdf) of this fluid mechanics presentation can be downloaded at www.drdavidnaylor.net
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluiddynamics

[@isagumus1]

Amazing explaination! Thank you a lot

[@FluidMatters]

Thanks for the kind words.

[@tytrinhcong8369]

Thank sir.

[@nghiadoan1239]

At the leaving control surface, why we need to write Vc(costheta) as Vc has already moved along the horizontal direction?

[@FluidMatters]

Recognize that the jet leaves the control volume with the same relative speed at is it came in with: (V_j-V_c). So, you have to take the horizontal component of that relative speed. Imagine the jet being turned through a full 90 degrees. In this hypothetical case, the jet would leave in the vertical direction relative to the moving control volume. So, with no horizontal component relative to the moving control volume. I find it helps to imagine what I would see if I was riding with the control volume. I hope that helps.

[@mariajoselealsabogal1962]

Excelente video

[@FluidMatters]

Thanks. Glad to hear it was helpful.

[@angeleduardoleovigildomarq7543]

what if the car has mass, or weight?

[@FluidMatters]

Cart is moving at constant velocity. So, the mass of the cart is not a factor. No acceleration.

[@r2k314]

I don't understand why you square the out velocity before multiplying by cosine. The out velocity is only the X-component. V^2 cosine is not a physically relevant quantity is it?

[@FluidMatters]

(V_j-V_c) is associated with the mass flow rate term. Also, (V_j-V-c) cos (theta) is the exit velocity. These two terms are multiplied together to get the rate of momentum out i.e., mass flow rate times relative velocity. That's why the relative velocity term is squared. I hope that helps.

[@ethiotechamharic4921]

please solve this problem.a water jet is turned through an angle of 180 dgree by the device shown in figure.the fluid stream has a constant diameter of 2cm.if the magnitude of the restraining force is 500kpa,estimate the average water velocity of the incoming water jet.do you think this is a realistic set of flow condition?why or why not?