Solving Flow Rate Through Pipes with Pressure Difference

AI Thread Summary
To solve for the flow rate of water through a horizontal pipe with varying diameters, the areas of the pipes are calculated using A = π(r)^2, resulting in 78.5 cm² for the larger pipe and 19.6 cm² for the smaller pipe. The forces in each section are determined using F = PA, yielding 6.28x10^6 N for the larger pipe and 1.18x10^6 N for the smaller. The discussion suggests using Bernoulli's equation, P1 + 1/2 * ρ * V1² = P2 + 1/2 * ρ * V2², along with the continuity equation A1V1 = A2V2 to find the velocities V1 and V2. The user expresses uncertainty about which kinematic equation to apply for velocity calculations. The conversation emphasizes the application of fluid dynamics principles to determine flow rates in pipes.
Husker70
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Homework Statement


A horizontal pipe 10.0cm in diameter has a smooth reduction to a pipe
5.00cm in diameter. If the pressure of the water in the larger pipe is
8.00x10^4Pa and the pressure in the smaller pipe is 6.00x10^4Pa, at
what rate does water flow through the pipes?

Homework Equations


A = pie(r)^2
Kinematics equation to find velocity
A1V1 = A2V2
F=PA

The Attempt at a Solution


I got areas first
A = pie(5.00cm)^2 = 78.5cm^2
A = pie(2.50cm)^2 = 19.6cm^2

Then I found F using F=PA
F = (8.00x10^4Pa)(78.5cm^2) = 6.28x10^6N
F = (6.00x10^4Pa)(19.6cm^2) = 1.18x10^6N

I'm not sure what kinematics equation to use to find velocity
Thanks,
Kevin
 
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Using Bernoulli's equation you can wright P1+1/2*p*V1^2 = P2 + 1/2*p*V2^2
By using the equation A1V1 = A2V2 you can solve for V1 and V2
 
I'll try it thanks
 

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