How Do You Calculate the Pressure Gradient in a Tube with Flowing Orange Juice?

[corinnab]

a very dilute orange juice flows along a smooth tube (0.010m in diameter) with a maximum flow rate of 0.1m/s.
a) State the assumptions needed to solve the problem
b) Calculate the pressure gradient

Equations:
Vmax = (Change in P * R^2)/(4*viscosity*L)

Reynolds number = (density*D*v)/viscosity

I am a bit confused about how to solve this as I havn't done any engineering before. This is what I have come up with so far:

a) Assume laminar flow - Reynolds number = 2100
Assume Newtonian fluid
Assume density of dilute orange juice is same as for water.

b) Use Reynolds number to solve for viscosity. Then solve for change in pressure/L using Vmax equation.

Any help would be appreciated!

 

[Chestermiller]

The Reynolds number is not always 2100 for laminar flow. You need to calculate the Re for this particular flow. Google Darcy-Weisbach correlation