The Equation of Continuity states that the mass flow rate has the same value at

Question

The Equation of Continuity states that the mass flow rate has the same value at every position along a tube that has a single entry and a single exit point for fluid flow. Basically it boils down to the idea that the fluid doesn’t magically disappear or appear. If 2.0 kg of fluid flows past a point in a tube in a time of 1.0 s, then 2.0 kg of fluid flows past another point in that tube in 1.0 s as well. If the tube is getting larger or smaller, the velocity adjusts to keep the mass flow rate the same. For a definition of mass flow rate, check the textbook. At Location One, fluid with a density of 7.83×102 kg/m3 is flowing at speed of 4.46 m/s through a circular pipe which has a radius of 1.050×10-1 m. As the fluid flows along the pipe, the pipe gets larger. At Location Two the pipe has a radius of 2.541×10-1 m (it is still circular in nature).

What is the cross-sectional area of the pipe at Location One?

What is the speed of the fluid at Location Two?

Explanation / Answer

FRom equation of continuity volume flow rate constant

volume flow rate V/t =A1v1 = A2v2

v1 = 4.46 m/s , r1 = 1.05*10^-1 m

A1 = pi*r^2 = 3.14*(0.105)^2 = 0.0346 m^2

v2 = (A1/A2)v1 = (r1/r2)^2*v1

v2 = (1.05/2.541)^2*4.46 =0.762 m/s

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