What rate does water flow through the pipes?

[brunettegurl]

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]

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.

 

[brunettegurl]

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]

P1 - P2 =1/2*ρ*v2^2 - 1/2*ρ*v1^2 = 1/2*m^2/ρ*(1/A2^2 - 1/A1^2)

 

[brunettegurl]

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]

I am getting 68644 m^3/s