Buckingham Pi Theory: Propeller & Pipe Flow Analysis for Jay

[jayjay112]

Hi I feel I am competent enough at the Buckingham Pi theory regarding both Pipe flow and for Propeller analysis.

Derive a relationship between the volume flow rate and rotational speed of propeller in terms of the diameter of the pipe and propeller and also fluid characteristics density and viscosity of the fluid.

For a flow through a closed, circular sectioned pipe which is metered by measuring the speed of rotation of a propeller having its axis along the pipe central line.

I am unsure how to start this problem? I am able to do dimensional analysis for both individually but I don't understand how to combine the two.

Can someone please suggest how to start?For Propeller the variables I have are: (d, u, p N, U)
d = diameter
u = viscosity
p = rho density
N = revolutions per s
U = advance speed

For Pipe: (delta P, V, D, e, v, p)
delta P = change in pressure
V = speed of flow
D = pipe diameter
e = roughness
v = viscosity
p = rho density
I really appreciate the help.
Jay

 

[fhoseinuk]

A large truck is to transport 30,000 Kg of orange pre-cooled to 4oC under average temperature of 27oC. The structure of the walls of the truck is such that the rate of heat transportation is UA=80W per oC temperature difference between the ambient and the oranges. From past experience, ambient air is estimated to enter the cargo space of the truck through the cracks at a rate of 4L/s. Also, the average heat of respiration of the oranges at 4oC is 0.017W/kg for this particular load. Disregarding any condensation and taking the density of air to be 1.15kg/m3, determine the refrigeration load of this truck and the amount of ice needed to meet the entire refrigeration need of the truck for a 15hour trip.

Can you help me on figuring out how to start this question?