Question

Consider the incompressible flow of water through a divergent duct. The inlet velocity and area are 5 ft/s and 10 ft^2, respectively. If the exit area Is 4 times the inlet area, calculate the water flow velocity at the exit.

Answer 1

Answer:

v₂ = 1.25 m/s

Explanation:

given,

inlet velocity, v₁ = 5 ft/s

inlet Area = A = 10 ft²

outlet velocity, v₂ = ?

outlet Area = 4 A

                  = 4 x 10 = 40 ft²

Using continuity equation

     A₁ v₁ = A₂ v₂

     10 v₁ = 40 v₂

  $v_2 = \dfrac{v_1}{4}$

  $v_2 = \dfrac{5}{4}$

       v₂ = 1.25 m/s

Hence, the exit velocity of the water through the duct is equal to 1.25 m/s.