## In the early seventeenth century Mersenne (1588–1648) conducted experiments with long lengths of rope and so obtained the law for the frequency of transverse vibrations of strings.

In the early seventeenth century Mersenne (1588–1648) conducted experiments with long lengths of rope and so obtained the law for the frequency of transverse vibrations of strings. Assuming that the frequency depends on products of powers of T, the tension in the rope, l, the length of the rope, and m, the mass per unit length of the rope,
i) find, by dimensional analysis, the form of the relationship. A rope of length 24 m and mass 0.5 kg m-1 under tension of 72 N is found to vibrate with a frequency of of a cycle per second.
ii) State the exact relationship between the frequency, T, l and m.
iii) Find the frequency of vibration of a string of length 20 cm and mass 0.005 g cm-1 under a tension of 8  105 dynes. (The dyne is the cgs unit of force: 1 dyne is the force required to give a mass of 1 g an acceleration of 1 cm s-2 .)

### 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….