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)

 

[Nino MMP]

and (b).To answer this question, you will need to first calculate the values of vmean and vy=0 for both cases. The formula for vmean is vmean = Q/A, where Q is the volumetric flow rate and A is the cross-sectional area. For case (a), the cross-sectional area is given by A = pi x (Dd/2)^2 (where pi = 3.14159). For case (b), the cross-sectional area is given by A = pi x (Dp/2)^2. Once you have calculated the values of vmean and vy=0, you can then plot the velocity profiles for both cases using the given equation.Once you have plotted the velocity profiles, you can then calculate the f and ΔP/L values using the Blasius equation f = 0.079Re-0.25. The Reynolds number for both cases is given as Re = 105, so you can then calculate the corresponding f and ΔP/L values for both cases.