In: Physics
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:????
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)