Fluid mechanics question

1. Aug 11, 2008

math_04

1. The problem statement, all variables and given/known data

Actually there are two questions in it.

First question is;

1) Determine the density 8km below the surface of the ocean where the pressure is 87.7Mpa, given that the density at the surface is 1025 kg m^-3 and the modulus of elasticity is 2.37GPa (use integration).

Second question is

2) If the velocity distribution in a 150mm diameter pipe carrying oil where mu(greek symbol)=0.048 Ns/m^2 and relative density = 0.913) is given by

u= 1.125 - 200(0.075-y)^2 where u denotes the velocity parallel to the boundary in m/s and y the distance from the solid boundary in m.

Calculate

a) The velocity gradient and the shear stress at the boundary and at a point 50mm from the boundary.
b) The shear stress at the centre of the line
c) The force resisting the fluid motion over a pipe length of 300m

2. Relevant equations

3. The attempt at a solution

For the first question, could you give me a hint where to start? It says use integration but on what? I have a formula which is dP/dz = -rho (greek symbol) x g. z is the height of the fluid element.

For the second question, I figured out part a. You differentiate u and plug in the values for y and mu in. I got the shear stress to be 0.48 Nm^-2. But I am not sure about the velocity gradient. Is it just du/dy and then plugging in the values for y (y=0.05m)? If so, how would the units pan out? Would it be m/s?

Looking at the answer for b which is 0, I am guessing there is some sort of law for shear stress at the centre of the pipe?

For c) i think I can work it out, just need to find the formula (hopefully!)

Thanks.