Apply the continuity equation in the following scenario to determine the fluid v

Question

Apply the continuity equation in the following scenario to determine the fluid velocity at the outlet of the pipe shown in the drawing below. State all reasonable assumptions and show ALL of your work, Ensure that you provide the appropriate units for your answer.

Working fluid: water at STP

Inlet mass flow rate: 500lbm/hr                        

inlet pipe diameter: 24 inches                        outlet pipe diameter: 9 inches

inlet fluid velocity: 200 feet/sec                        Outler fluid velocity:????

Explanation / Answer

From equation of continuity, :

a1*v1 = a2*v2                               -------------------------1

a1 = area of cross section of pipe at inlet point

a2 = area of cross section at outlet point

v1 = velocity of flow of liquid at inlet point = 200 feet/ sec

v2 = velocity at outlet point = ?

from eq. 1:

pie*(D1/2)2*v1 = pie*(D2 / 2)2*v2                                      ( area, a = pie*r2 = pie* ( Dia/2)2 )

D12 *v1 = D22 *v2

242* 200 = 92 *v2

v2 ( outer fluid velocity) = 1422.2 feet/ sec

                          or     = 433.54 m/s                                ( 1ft = 0.3048m)

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