Posted by **flame** on Friday, September 24, 2010 at 1:46am.

A horizontal pipe 17.00 cm in diameter has a smooth reduction to a pipe 8.50 cm in diameter. If the pressure of the water in the larger pipe is 8.00 104 Pa and the pressure in the smaller pipe is 6.00 104 Pa, at what rate does water flow through the pipes?

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**MathMate**, Friday, September 24, 2010 at 10:02am
Use bernoulli's equation

p+ρV²+ρgh=constant

for each of the sections.

p=pressure

ρ=density

V=velocity

The ρgh term can be neglected if the pipe is horizontal.

The continuity equation gives

A1V1=A2V2, where

V1, V2, A1 and A2 are the velocities and cross sectional areas of the corresponding sections.

So we have two unknowns V1 and V2, and two equations

p1+ρV1²=p2+ρV2² ...(1)

V1*A1=V2*A2 ....(2)

Solve for V1 and V2.

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**flame**, Sunday, September 26, 2010 at 8:57pm
how do i convert the answer to kg/s

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**MathMate**, Monday, September 27, 2010 at 9:44am
Flow is given by the product of the water velocity (m/s) and cross sectional area (m²), multiplied by the density ρ (1000 kg/m³).

or,

Q=A1*V1*ρ

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