Water is flowing in a pipe of varying cross-sectional area...

Question

Water is flowing in a pipe of varying cross-sectional area, and at all points the water completely fills the pipe. The cross-sectional area at point 1 is 0.0825 m2, and the velocity is 3.29 m/s. Compute the fluid's velocity at point 2 where the cross sectional area is 0.0471 m2.

Answer 1

The appropriate equation is that of continuity (for constant density, the stipulation that mass cannot accumulate means that volumetric flow is constant)

Rate of liquid volume flow = v*A = constant v is velocity and A is area

v₁A₁ = v₂A₂ or v is proportional to 1/A

v₂ = v₁(A₁/A₂) plug in values (proportional problems like these, you can use any units for v and A as long as they are the same for a particular quantity)

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