Cox’s formula: Assume that a long horizontal pipe connects the bottom of a reservoir with a drainage area. Cox’s formula provides a way of determining the velocity v of the water flowing through the...

Cox’s formula: Assume that a long horizontal pipe connects the bottom of a reservoir with a drainage area. Cox’s formula provides a way of determining the velocity v of the water flowing through the pipe:

Here H is the depth of the reservoir in feet, d is the pipe diameter in inches, L is the length of the pipe in feet, and the velocity v of the water is in feet per second. (See Figure 5.103 on the following page.)

a. Graph the quadratic function 4v2 + 5v − 2 using a horizontal span from 0 to 10.

b. Judging on the basis of Cox’s formula, is it possible to have a velocity of 0.25 foot per second?

c. Find the velocity of the water in the pipe if its diameter is 4 inches, its length is 1000 feet, and the reservoir is 50 feet deep.

d. If the water velocity is too high, there will be erosion problems. Assuming that the pipe length is 1000 feet and the reservoir is 50 feet deep, determine the largest pipe diameter that will ensure that the water velocity does not exceed 10 feet per second.