Finding pipe radius from water flow rate and manometer heights

[michaelw]

Water (h=1.00×10–3 Pa·s) is flowing through a horizontal pipe with a volume flow rate of 0.014 m3/s. As the drawing shows, there are two vertical tubes that project from the pipe. From the data in the drawing, find the radius of the horizontal pipe.

I don't have a clue how to start this
Please guide me to the right path :)

 

[michaelw]

anyone have a clue ?

 

[FredGarvin]

The diagram is telling you what the pressure drop along the pipe is, i.e. the $$\Delta P$$ Also you are given the flow rate and viscosity. That means you are interested in the equation for viscous flow without any minor losses. If you use an energy balance you should end up with an equation looking something like:

$$P_{1} - P_{2} = f (\frac{L}{D})(\frac{\rho V^2}{2})$$

You can then get an equation with D being a function of friction factor and an equation with Reynolds number as a function of diameter. From that point on you'll have to iterate a soulution taking guesses at the friction factor. That will give you a way to calculate D and Re. Once you do that you can compare the friction factor calculated vs. the one you guessed. When they are very close, you will have your diameter. Oh yeah, since it wasn't listed in the problem, you'll have to make an assumption on the relative roughness of the pipe.