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 8.24×102 kg/m3 is flowing at speed of 3.36 m/s through a circular pipe which has a radius of 1.030×10-1 m. As the fluid flows along the pipe, the pipe gets larger. At Location Two the pipe has a radius of 2.719×10-1 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?

Answer 1

At location 1 :

A₁ = area of cross-section = $\pi$ r² = 3.14 (0.103)² = 0.033 m²

v₁ = 3.36 m/s

At location 2 :

A₂ = area of cross-section = $\pi$ r² = 3.14 (0.2719)² = 0.232 m²

v₂ = ?

Using equation of continuity

A₁ v₁ = A₂ v₂

0.033 x 3.36 = (0.232) v₂

v₂ = 0.478 m/s