How to Calculate Flow Rate in a Tapered Pipe with Pressure Difference?

AI Thread Summary
To calculate the volume flow rate of alcohol in a tapered pipe with a pressure difference of 8.8 kPa, the relevant equations include Bernoulli's equation and the continuity equation. The cross-sectional areas are given, with A1 at 43.7 cm² and A2 at A1/4. The density of the alcohol is 796 kg/m³. By substituting the velocity from the continuity equation into Bernoulli's equation, one can solve for the flow rate. The discussion emphasizes the need to derive the relationship between velocities and pressures to find the volume flow rate.
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Homework Statement


An alcohol flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 43.7 cm2 to A2= A1/4. The pressure difference Δp between the wide and the narrow sections of the pipe is 8.8 kPa. What is the volume flow rate ΔV/Δt of the alcohol? The density of the alcohol is ρ = 796 kg/m3.


Homework Equations


I figured I would have to use:

v1 = sqrt( 2*deltap / 15(rho) )


The Attempt at a Solution



I'm not entirely sure how to start this. I'm very cinfused.

v^2
 
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Hi 12342, welcome to PF.
The relevant equations are
P1 +1/2*ρ*v1^2 = P1 + 1/2*ρ*v2^2 ...(1)
And rat of flow
Q = A1*v1 = A2*v2...(2)
From the second equation find v2 in terms of v1 and put it in eq. 1. Then solve for v1and then Q.
 

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