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A power-law fluid has a density of 1075 kg/m3. It is pumped at a rate of 2500 kg/hour through a pipe of internal diameter 25 mm.The flow is laminar and the power law constants are K2 = 3 Pa.s^n and n = 0.5. Estimate the pressure drop over a 10 m straight length of pipe and the centre-line velocity for these conditions.

Okay, so i believe i have calculated the center line velocity as follows. My problem is, i am unsure of how to calculate the pressure drop across the length of the pipe.

Power law = shear stress = K(du/dy)^n

mass flow rate = density * area*velocity

therefore: (after calculating area and dividing mass flow rate by 3600)

V = 0.6944 / 1075 * 0.000491 = 1.3156 m^3s^-1

Now, im unsure how to proceed. Im guessing the power law equation has some thing to do with the pressure change.

Im thinking about using bernouilles equation, but there isnt enough information for me to use it. So im guessin i have to use the power law model in order to gaather enough data.

thank you.