Problem 9 A fire-hose is connected to a fire-hydrant at street level. The gauge

Question

Problem 9 A fire-hose is connected to a fire-hydrant at street level. The gauge pressure at the fire-hydrant is 12atm and the diameter of the outlet of the fire-hydrant is 12.0 cm. The nozzle is connected to the fire-hose has a diameter of 4.0cm. Tom, the fire fighter, takes the nozzle up the building to the third floor, so that the nozzle is 30m above the street level. i)What is the gauge pressure at the nozzle, when the nozzle is turned off and the water does not flow.? ii) Next, the hose is turned on, and the gauge pressure at the fire hydrant remains 12atm. Determine the speed of the flow at the fire-hydrant and at the hose.

Explanation / Answer

i) at the nozzle

P =12 atm

gauge pressure = 12 * 1.01 *10^5 - 1000 * 9.8 * 30

gauge pressure = 9.18 *10^5 Pa

the gauge pressure at the nozzle is 9.18 *10^5 Pa

ii)

let the speed of flow at hose is v

Using equation of continuity

speed of flow at fire hydrant = v * 4^2/12^2 = v/9

Using Bernoulli's equation

12 * 1.01 *10^5 + 0.50 * 1000 * (v/9)^2 = 1000 * 9.8 * 30 + 0.50 * 1000 * v^2

solving for v

v = 43.11 m/s

the speed of flow at hose is 43.11 m/s

speed at fire hydrant = 43.11/9 = 4.79 m/s

speed at fire hydrant is 4.79 m/s

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