Bournalli's Equation homework problem

AI Thread Summary
In the discussion about Bournalli's Equation, the problem involves a fluid flowing through a horizontal pipe with varying diameters. The derived pressure at Point 2 is confirmed as P2 = P1 - 40(rho)v^2. Participants debate the implications of pressure versus velocity, noting that while P1 has higher pressure, the higher velocity at Point 2 could result in a more painful impact. This leads to a conclusion that despite lower pressure at Point 2, the force of the fluid exiting a smaller diameter could be more intense. The discussion highlights the counterintuitive relationship between pressure and velocity in fluid dynamics.
jan2905
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A fluid of density (rho) flows through a horizontal pipe with negligible viscosity. The flow is streamline with constant flow rate. The diameter of the pipe at Point 1 is d and the flow speed is v. If the diameter of the pipe at Point 2 is d/3, then the pressure at Point 2 is?



Bournalli's Equation (sp). I ended up getting P2=P1 - 40(rho)v^2. Correct?
 
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jan2905: That is correct; p2 = p1 - 40*rho*v^2.
 
would this mean that if i were hit with the liquid at the respective points...

p1 would hurt more than p2? that would mean that a large mouth waterhose has more force than a small mouth... that is not correct though.
 
jan2905: I think water exiting a small-mouth water hose at point 2 would probably hurt more, because it has a much higher velocity than the water at point 1. Both streams would be at atmospheric pressure immediately upon exit from the nozzle.
 
but we deduced that p1 would have more pressure therefore hurting more. this math seems to be counterintuitive.
 
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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