If the geometry of a flow channel and the parabolic velocity profile of the fluid flowing through it are known, is there any method (equation) to calculate an equivalent uniform velocity profile through the same channel?
I agree with @ Devraj Chauhan . Expressing the same in different analogy,
Q=Volume of fluid flowing through channel per sec or Volume flow rate
Q=Vol/sec = m3/sec =m2 * m/sec = A * U
[Where m3= meter-cube,m2=meter-square,A=Cross-Sectional area of Channel,U=uniform velocity of fluid flowing along the channel]
U=Q/A =Volume flow rate/A.
Even though,The volumetric flow rate can be calculated by integrating the parabolic velocity profile but limits of integration depends on the geometry of the flow channel,when proper limits [by careful setting] are substituted in the integral, evaluation of integral and further division with cross-sectional area yields Uniform Velocity.