Turbulent flow velocity profiles

[suvernfraggle]

i've been given this question by my lecturer at university and I am struggling with where to start with it to be honest. it feels like i don't have enough information. please can someone help?

For turbulent flow, the velocity profile inside a duct and a pipe of diameters Dd and Dp and
both with distance y from the centre line is: vy/vy=0 = (1-y/r)1/7, where vy=0 = vmean/0.817 and vmean=Q/A. Plot the velocity profiles for:

(a) Air flowing in a duct measuring Dd = 0.6m and with Re = 105.
(b) Water flowing in a pipe measuring Dp = 0.5m and with Re = 105.
(c) Calculate the vmean and vy=0 for both cases (a) and (b)
(d) If the Blasius equation f = 0.079Re-0.25 applies, calculate the values of f and ΔP/L for (a)

 

[Valkarie]

and (b).To answer this question, you will need to start by calculating the mean velocity (vmean) for each case (a) and (b). This can be done using the equation given: vmean = Q/A, where Q is the volumetric flow rate (in m3/s) and A is the cross-sectional area of the duct or pipe (in m2). Once you have calculated vmean, you can then calculate vy=0 (the average velocity at the centre line) using the equation: vy=0 = vmean/0.817.Next, you will need to plot the velocity profiles for both cases (a) and (b). To do this, you will need to calculate the value of 'r' (the radius of the duct or pipe) for each case. Then, using the equation vy/vy=0 = (1-y/r)1/7, you can calculate the values of vy/vy=0 for different distances y from the centre line (i.e. 0, 0.1, 0.2 etc.). These values can then be plotted on a graph against y to give the velocity profile for each case.Finally, to calculate the values of f and ΔP/L for each case, you will need to use the Blasius equation f = 0.079Re-0.25. Here, Re is the Reynolds number for each case (which you should already have calculated), and f is the friction factor. The value of ΔP/L can then be calculated using the equation ΔP/L = 4fLvmean2/D, where L is the length of the duct or pipe (in m), and D is the diameter of the pipe or duct (in m).