Why Are Pressure Forces on a Control Volume Neglected in Vane Analysis?

[nanunath]

Force exerted on a Fixed Vane...Plz help?

Hi everyone...:)


Consider :- "The general Impulse momentum equation for a Control Volume"

F = M₁+M₂

F is the sum of all external forces acting on the Control volume{CV}...
so applying this to a jet impinging on a fixed curved vane ...
I think the external forces on the CV are:
1) End pressure forces [at start and end of the CV...{please download http://www.fzuploads.com/files/10/9/1255081847-sridhar1867-Reference-FM-Streeter.rar.rar" to refer to CV taken here...or any other references needed for this} and the pressure force acting due to the surrounding atmosphere.
2) Force on CV by Vane.{this is alright for me}

But none of the texts ever accounts for the pressure forces exerted on a the CV in case of vane [I think more specifically...zero gauge pressure flow,and neglecting change in elevation at the end Control sufaces,neglecting friction]...WHY arent the pressure forces considered here...

Can anyone help me as to where am I exactly messing up..Plz?.. :( :(....

In the rare case you need any quick revision on the basics please http://www.fzuploads.com/files/10/9/1255081847-sridhar1867-Reference-FM-Streeter.rar.rar"...In the rar file I have included as to how the "General Control volume conservation equation","General Impulse momentum equation" are derived in the book I use-"FM by V.L.Streeter" and also the section "Force exerted on a vane" .

Any help Welcome...:)

Thanks!...:)

 

[Achy47]

Hi there,

I understand your confusion and concern regarding the pressure forces exerted on a fixed curved vane. Let me try to explain why these forces are not usually considered in this scenario.

First, let's clarify the concept of a control volume. A control volume is an imaginary boundary that encloses a specific region of interest, where we can apply the principles of conservation of mass, momentum, and energy. In the case of a jet impinging on a fixed curved vane, the control volume would be the region surrounding the vane, where the jet flow is affected by the presence of the vane.

Now, let's consider the forces acting on this control volume. As you mentioned, there are two main external forces: the end pressure forces and the force exerted by the vane. The end pressure forces are the forces exerted by the fluid on the control volume boundaries, and they are taken into account in the general impulse momentum equation for the control volume, as you have correctly stated.

However, in the case of a fixed curved vane, the pressure forces exerted by the fluid on the vane itself are not considered because they are internal forces. These forces are already included in the force exerted by the vane on the control volume. In other words, the vane is considered as part of the control volume, and the force it exerts on the fluid is already taking into account the pressure forces exerted by the fluid on the vane.

I hope this clarifies your doubts. If you need further assistance, please feel free to refer to the references you have provided or reach out to a colleague with expertise in this area. Keep up the good work in your research!