Question

A 1.0 cm diameter pipe widens to 5.0 cm, then narrows to 0.7 cm. Liquid flows through the first segment at a speed of 8.0 m/s. (a) What is the speed in the second and third segments? second segment m/s third segment m/s (b) What is the volume flow rate through the pipe? m3/s

Answer 1

(a) What is the speed in the second and third segments?

using equation of continuity, we have

A₁ v₁ = A₂ v₂ = A₃ v₃

( $\pi$ r₁²) v₁ = ( $\pi$ r₂²) v₂ = ( $\pi$ r₃²) v₃

r₁² v₁ = r₂² v₂ = r₃² v₃

(0.005 m)² (8 m/s) = (0.025 m)² v₂ = (0.0035 m)² v₃

v₂ = [(0.005 m) / (0.025 m)]² (8 m/s)

v₂ = 0.32 m/s

And

v₃ = [(0.005 m) / (0.0035 m)]² (8 m/s)

v₃ = 16.3 m/s

(b) What is the volume flow rate through the pipe?

we know that,   Q = A₁ v₁ = ( $\pi$ r₁²) v₁

Q = (3.14) (0.005 m)² (8 m/s)

Q = 6.28 x 10^-4 m³/s