Water moves through a constricted pipe in steady, ideal flow. At the lower point

Question

Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is 1.65 105 Pa and the pipe radius is 2.80 cm. At the higher point located at y = 2.50 m, the pressure is 1.27 105 Pa and the pipe radius is 1.60 cm. (a) Find the speed of flow in the lower section. m/s (b) Find the speed of flow in the upper section. Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (c) Find the volume flow rate through the pipe. m3/s

Explanation / Answer

This seems like a straight up Bernoulli problem

P1 + 1/2*rho*v1^2 + rho*g*h1 = P2 + 1/2*rho*v2^2 + rho*g*h2

or

P1/rho + 1/2*v1^2 + g*h1 = P2/rho + 1/2*v2^2 + h2

Another concept is mass flow, i.e. the volume of water that moves through point 1 also moves through point 2.

mass flow1 = mass flow2

rho*Volume flow1 = rho*Volume flow2

volume flow = Cross sectional Area * v

A1*v1 = A2*v2

v2 = A1/A2*v1

Sub that into the Top equation and solve for v2

P1/rho + 1/2*v1^2 + g*h1 = P2/rho + 1/2*(A1/A2*v1)^2 + h2
1/2*v1^2 - 1/2*(A1/A2*v1)^2 = (P2-P1)/rho + g*(h2-h1)
v1^2(1/2 - 1/2*(A1/A2)^2) = (P2-P1)/rho + g*(h2-h1)
v1^2 = (P2-P1)/rho + g*(h2-h1) / (1/2 - 1/2*(A1/A2)^2)
v1 = sqrt( (P2-P1)/rho + g*(h2-h1) / (1/2 - 1/2*(A1/A2)^2))

Remember to use correct units.
BTW
A = d^2/4*pi

I got
A) v1 = 1.157 m/s
B) v2 = A1/A2*v1 = 5.856 m/s
C) Volume flow = v1*A1 = v2*A2 = 0.000662 m^3/s

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