How Do You Calculate Water Speed in a Pipe Using Bernoulli's Principle?

AI Thread Summary
To calculate water speed in a pipe using Bernoulli's Principle, start by applying the equation P + 1/2pv^2 = constant, where P is pressure and v is velocity. The continuity equation, A1v1 = A2v2, relates the cross-sectional areas and velocities at two points in the pipe. Given the pressures and areas, first solve for one velocity using the continuity equation, then substitute it back into Bernoulli's equation to find the second velocity. It's crucial to ensure all units are consistent and to carefully track the algebraic manipulation to avoid errors. Detailed calculations and clear steps will help clarify the solution process.
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I have this problem:
Water flowing in a horizontal pipe is at a pressure of 1.5 105 Pa at a point where its cross-sectional area is 1.50 m2. When the pipe narrows to 0.400 m2, the pressure drops to 1.16 105 Pa.
(a) Find the water's speed in the wider pipe
(b) Find the water's speed in the narrower pipe.

I tried using Bernoulli's Principle but I can't get it.
I took the (p)(g)(h) out of both sides since the pipe's height doesn't change. And then I tried solving for v1 and v2 but there are two unknowns and I don't know what to do after that...

If anyone could help, that would be awesome.
Thanks in advance.
 
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HINT: The flow is horizontal so gravity is not a consideration. You have Bernoulli's Principle to work with (pressure + kinetic energy per unit volume = constant) but you also have a continuity condition (flux times cross section = constant).
 
Hi, thanks for the info.

I tried using the equation, P + 1/2pv^2 = P + 1/2pv^2
and I ended up with two unknowns, the two different v^2.
So then I tried solving for 1 v using the AV=AV equation and then plugging it back into the first equation but that didn't come out right either...


Anymore suggestions?
Could anyone show me where I am messing this up?
 
You're approach seems correct. Show the details of your calculation.
 

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