Bending force at suction inlet? 1

[novis76]

Hello, this is perhaps a stupid question but my mind is playing tricks on me.

At a discharge pipe outlet a stationary force equal to F=m*V creates a bending torque at the support.

If the flow is reversed - what force/torque is developed and in what direction?

Please see attached figure

Thanks

 

[cvg]

why not draw your free bodies and see if that doesn't clear it up?

 

[novis76]

cvg, given Vel=10m/s (314.15 kg/s @ rho=1000, A=0.2^2*pi/4) and P_atm=0 bar(g), D1=D2=0.2 m (0.65 ft), rho=1000 kg/m^3

Pressure inside pipe
Discharge: P1=P2 = P_atm = 0
Suction (smooth inlet): P1=P2 = P_atm - 0.5*rho*V^2 = 0 - 0.5*1000*10^2 = -50000 Pa

Force Fx,Fy
Fx=m*V*sin(90º)+p*A*sin(90º)
Fy=m*V*(1-cos(90º)) + p*A*(1-cos(90º))

Discharge: Fx = 314.15*10*1+0*0.031415*1 = 3142 N
Fy = 314.15*10*(1-0)+0*0.031415*(1-0) = 3142 N

Suction: Fx = -314.15*10*1+(-50000)*0.031415*1 = 1570 N
Fy = -314.15*10*(1-0)+(-50000)*0.031415*(1-0) = 1570 N

Is this correct? Is the force during suction only half for discharge? Somehow I always imagined the force would be equal.

 

[Sch10Sean]

Hi, very interesting question. However, I think you made two mistakes. One arithmetic and one more basic. According to your calculation Fx and Fy should be -4712 N and not -1570 N. A negative value indicates a reaction force inwards, towards the bend.

Furthermore, due to the fact that the inflow into the pipe is not perpendicular to the inlet the usual "momentum method" is not straightforward to use.

I had a similar problem myself. I was asked to approximate the force on the suction side of a pump. My conclusion was that there is a outward force (same direction as during discharge) with a magnitude of F=m*V-p*A.

 

[chicopee]

Per your diagrams in your OP, both moments will be in the same direction but not necessarily of the same magnitude because the horizontal pressures before the bends will be greater than the vertical pressures after the bends. The directions of the moments will be counterclockwise and their magnitudes determined only from the horizontal pressure components.

 

[novis76]

chicopee and Sch10Sean, thank you both for your answers. If I understand you correctly you both say that the force is directed in the same direction as when the pipe discharges. That is really interesting because it is the opposite what to expect using the momentum change method that is used during discharge (but I understand Sch10Sen:s argument that the flow isn't perpendicular and therefore invalid)

@Sch10Sean: I noticed my aritimetic mistake, thanks. My problem also involves a pump inlet but I wanted to simplify my question. I think I understand how you came up with your force but if you could (or someone else) explain it to me I would be grateful. Thanks again.

 

[waterpipe]

Yes. The forces are in the same direction and magnitude. here's a free force diagram independent of the flow direction.

If you want to "feel" it, then consider the discharge scenario. Flow "hits" the bend (fy) and there is a force at the exit (fx). Since it is anchored at the bottom in your case, there's a momentum at the anchor point. Now, consider the suction scenario: Flow hits the bend (fx) and there is a force at the exit (fy).

BTW, if you consider the dynamic pressure(0.5*rho*V^2) in your calculations, then you should consider it for the both scenarios. You've considered this for suction condition but not for the discharge. that's why the forces in two scenarios are different in your calculations. In reality, they are the same provided the discharge condition is the same, i.e same pressure (if you are dealing with fluid, same fluid level).

And the final note, Patm is not zero. it is 100kpa. make sure that you keep your pressure reference the same along all your calculations if you assume Patm=0.

Hope this would be helpful.

 

[chicopee]

Waterpipe, I am not sure that both torques will have the same magnitude, since in one case, the fluid will be pushed and the second case, the fluid will be aspirated; even if their flows have the same magnitude, their temperatures will be slightly different even if the source reservoir temperature is constant.

 

[waterpipe]

Chicopee, I've consider that the temperature be the same and I commented considering water as the medium fluid. I'm not sure if I can understand why the temp could be different in two scenarios but the difference would show it in the concerned calculation via changes in water density which i suspect to play an important role.

I have to add that mu assumption was for an identical pipe diameter through the discharge pipe, otherwise the forces differ in the reverse flow direction.

I hope that the following solved problems clear up the case for OP. You can try to solve them for the reverse direction for a better understanding. Both examples are from the book "Fluid Mechanics With Engineering Applications- Finnemore & Franzini".

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