Chapter 1.4, Problem 25E

Reminder:-Round all answers to two decimal places unless otherwise indicated.

Head and Pressure Determining the water pressure at a given location employs the concept of the head, which is the vertical distance, in feet, from the surface of a source body of water to the location. The pressure exerted by water is proportional to the head. If we measure head in feet and pressure in pounds per square inch, then the constant of proportionality is the weight of a column of water that is 1 foot high and 1 inch square at the base. That much water weighs $0.434$ pound (See figure $1.57$.)

FIGURE $1.57$

a. Write an equation that expresses the proportionality relationship between pressure $p$ and head $h$.

b. For a pumper truck pumping water to a fire, the back pressure is the additional pressure on the pump caused by the height of the nozzle. Consider a pumper at street level pumping water through a hose to firefighters on the top of the eighth floor of a building. If each floor is $12$ feet high, what is the head of water at the mouth of the nozzle? What is the back pressure on the pumper? (Another way of thinking of back pressure is as the minimum pressure the pumper must produce in order to make water flow out the end of the nozzle.)

c. Head (and therefore back pressure) depends only on the height of the nozzle above the pumper. It is affected neither by the volume of the water nor by horizontal distance. A pumper in a remote location is pumping water to firefighters on the far slope of a hill. At its peak, the hill is $185$ feet higher than the pumper. The hose goes over the hill and then down the hill to a point $40$ feet below the peak. Find the head and the back pressure on the pumper.