## Suppose a straight tube could be drilled right through the Earth, modelled as a uniform sphere of radius R and total mass M. A ball of unit mass is dropped into the tube at the surface of the Earth.

A body of unit mass inside a uniform sphere at a distance r from its centre O experiences a gravitational attraction towards the centre of where G is the gravitational constant and Mr is the mass of material inside the sphere of radius r.
(In other words it is as if the body were on the surface of a sphere of radius r, all the matter further from the centre than r will have no net gravitational effect on the body.) Suppose a straight tube could be drilled right through the Earth, modelled as a uniform sphere of radius R and total mass M. A ball of unit mass is dropped into the tube at the surface of the Earth.
i) Work out the mass of a sphere of the Earth of radius r, in terms of R, M and r.
ii) Write down an expression for the gravitational force on the ball when at a distance r from the centre.
iii) Hence show that the ball will oscillate with simple harmonic motion with an amplitude equal to the radius of the Earth. Determine the period.

### In Problem 5.13.1, what throughputs can be achieved when pumping gasoline alone?

In Problem 5.13.1, what throughputs can be achieved when pumping gasoline alone? Use a specific gravity of 0.74 and viscosity of 0.65 for gasoline at the flowing temperature. Compare the….

### A pipeline 150 miles long from Beaumont pump station to a tank farm at Glendale is used to transport Alaskan North Slope crude oil (ANS crude).

A pipeline 150 miles long from Beaumont pump station to a tank farm at Glendale is used to transport Alaskan North Slope crude oil (ANS crude). The pipe is 20….

### The pipeline described in Problem 6.7.1 is used to batch ANS crude along with a light crude (0.85 specific gravity and 15 cSt viscosity at 60°F). Determine the optimum batch sizes to reduce pumping costs based on a 30 day operation. Consider a flow rate of 6000 bbl/hr.

The pipeline described in Problem 6.7.1 is used to batch ANS crude along with a light crude (0.85 specific gravity and 15 cSt viscosity at 60°F). Determine the optimum batch….