Where Could the Error Be in My Momentum Equation Calculation?

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The discussion centers on identifying errors in a momentum equation calculation that resulted in an approximate 2000N discrepancy from the correct answer. Key points of confusion include the use of an incorrect volume flow rate value and potential misinterpretation of the velocity terms in the Bernoulli equation. Additionally, there is a suggestion to consider only the mass of the water, rather than the combined mass of the water and pipe, when calculating the gravitational force. Clarifications about the orientation of the pipe and the nature of the pressure at the inlet being static are also raised. The conversation emphasizes the importance of precise values and interpretations in fluid dynamics calculations.
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I have attached the question and working out as i would lose the format. The answer i arrive at is innacurate by 2000N approx from the correct answer, If anybody could look at my working out and point out any mistakes i would appreciate it as i have been on this for hours and can't see the mistake

Thanks
 

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A couple of things: Did you use .355 instead of the given .335 for the volume flow rate when calculating the speeds c1 and c2?

In the Bernoulli equation, did you get the signs of the velocity terms correct?

I'm not sure, but shouldn't you use the mass of just the water rather than the total mass of water and pipe (240 kg) for the gravity force on the water in the equation for Fy?

[EDIT: To me, the question is not very clear as to whether the pipe bends upward or downward.]

[EDIT: Also, the pressure given at the inlet is given as "static".]
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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