# What rate does water flow through the pipes?

## Homework Statement

A horizontal pipe 10.9 cm in diameter has a smooth reduction to a pipe 4.50 cm in diameter. If the pressure of the water (density = 1000 kg/m3) in the larger pipe is 7.50×104 Pa and the pressure in the smaller pipe is 5.70×104 Pa, at what rate (as mass per unit time) does water flow through the pipes?

## Homework Equations

Bernoulli's equation. Po+1/2(rho)v^2+(rho)gh= pfinal +1/2(rho)vfinal^2+(rho)(g)(h final)

## The Attempt at a Solution

if i sub in the necessary parts we know that h will be the same so that becomes a constant. Po is 7.50×104 Pa and Pfinal is 5.70×104 Pa so if we simploify the above equation we get P1-P2 = ½$$\rho$$v22-½$$\rho$$v12.so i solved for $$\Delta$$v by $$\sqrt{\frac{P1-P2}{0.5*\rho}}$$ i got an answer of 6 but am unsure of the units to put in the answer..if this is actually the right working..pls. help

rl.bhat
Homework Helper
The rate of flow of water can be written as
m = Avρ
m^2 = A^2*v^2*ρ^2
1/2*m^2/A^2*ρ = 1/2*ρ*v^2
Substitute this value in the equation to find m.

i'm a little confused what value am i substituting in the equation to find m??and if i use the equation 1/2*m^2/A^2*ρ = 1/2*ρ*v^2

(m2/A2)*(1000)= (1000)v2

would my A= sum of both pipes diameter ....and what would v equal???l

rl.bhat
Homework Helper
P1 - P2 =1/2*ρ*v2^2 - 1/2*ρ*v1^2 = 1/2*m^2/ρ*(1/A2^2 - 1/A1^2)

P1 - P2 = 1/2*m^2/ρ*(1/A2^2 - 1/A1^2)
delta p =18000
A1= 9.331x10^-3
A2= 1.5904 x10^-3

i sub it in and get a value of 137030.15 ..does that look right??

rl.bhat
Homework Helper
I am getting 68644 m^3/s