AP Physics fluids and solids homework help

Question

A horizontal pipe of diameter 0.985 m has a smooth constriction to a section of diameter 0.591 m . The density of oil flowing in the pipe is 821 kg/m3 .

If the pressure in the pipe is 7270 N/m2 and in the constricted section is 5452.5 N/m2 , what is the rate at which oil is flowing?

Answer 1

The speed is different at the two ends. I assume you want to solve for the two speeds. I will set this up for you. Assuming steady incompressible flow with energy conservation,

ρv₁²/2 + P₁ = ρv₂²/2 + P₂

A₁v₁ = A₂v₂

You know ρ, P₁, and P₂. Get A₁ and A₂ form the given diameters using

A = πd²/4

That leaves you with a system of two equations in two unknowns v₁ and v₂, which you can solve.