A1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. liquid flows through the first segment at a speed of 8.0 m/s.
a: what is the speed in the second segment? /s
b: what is the speed in the third segment? /s
c: what is the volume flow rate through the pipe? l/s

Answer

given,

diameter of segment 1, d₁ = 1 cm

diameter of segment 2, d₂ = 2 cm

diameter of segment 3 , d₃ = 0.5 cm

speed of liquid in first segment, v₁ = 8 m/s

a) using continuity equation

      A₁ v₁ = A₂ v₂

      v₂ = 2 m/s

speed in the second segment = 2 m/s

b) again, using continuity equation

      A₂ v₂ = A₃ v₃

      v₂ = 32 m/s

speed in the second segment = 32 m/s

c) Flow rate in the pipe

    Q = A₁ V₁

      Q = 6.28 x 10⁻⁴ m³/s

       Q = 62.8 L/s

discharge in the pipe is equal to 62.8 L/s