# Fluid Mechanics - Turbulent flow velocity profile

• 1trumpet

#### 1trumpet

Hi

I'm a mechanical engineering student who has been set a question by my fluid mechanics lecturer. I need to plot the velocity flow profile of water flowing in a pipe. The information given in the question is

diameter = 0.5m
Re = 10^5

I know that the seventh power law is used to find velocity profile, but I can't see how I can use it without knowing max velocity, and I can't see how I can find max velocity without knowing dynamic viscosity or flow rate.

Am I thinking about this the wrong way? I would appreciate if anyone could point me in the right direction.

Thanks.

Reynolds Number = (pVD) / μ

Where p = density of fluid, V = mean velocity, D = hydraulic diameter, μ = dynamic viscosity.

We know all of those factors aside from V. So you can work out the mean velocity, which should give you the flow rate.

For dynamic/kinematic velocity: http://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html

I'm not sure if there's anything to work out though. Do you need an accurate plot based on figures or just show the basic flow pattern?

If you know the reynolds number, you know the type of flow within the pipe. From that you should know what type of pattern to expect and you could show the expected profile.

The dynamic viscosity depends on temperature, which is not given. Or are you suggesting I should assume ambient temperature?

Yes, it is already mentioned in the question that it is turbulent flow, so I know what the pattern should look like. An accurate plot is what I'm after.

I'd appreciate it if you could provide the full question for reference.

So far as temperature goes, I'd prefer to see the question. But I would probably assume ambient.

Here is the question in full:

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/7)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)

was there an answer to this question??