Discharge from a fire hose: The discharge of a fire hose depends on the diameter of the nozzle. Nozzle diameters are normally in multiples of 1 8 inch. Sometimes it is important to replace several hoses with a single hose of equivalent discharge capacity. Hoses with nozzle diameters d1, d2,...,dn have the same discharge capacity as a single hose with nozzle diameter D, where
a. A nozzle of what diameter has the same discharge capacity as three combined nozzles of diameters 11 8 inches, 15 8 inches, and 17 8 inches? You should report your answer as an available nozzle size, that is, in multiples of 1 8 .
b. We have two 1-inch nozzles and wish to use a third so that the combined discharge capacity of the three nozzles is the same as the discharge capacity of a 21 4 -inch nozzle. What should be the diameter of the third nozzle?
c. If we wish to use n hoses each with nozzle size d in order to have the combined discharge capacity of a single hose with nozzle size D, then we must use
How many half-inch nozzles are needed to attain the discharge capacity of a 2-inch nozzle?
d. We want to replace a nozzle of diameter 21 4 inches with 4 hoses each of the same nozzle diameter. What nozzle diameter for the 4 hoses will produce the same discharge capacity as the single hose?