Question

What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of 38 m ?

Express your answer to two significant figures and include the appropriate units.

P = ____ Pa

Answer 1

in this case, we have to use Bernoulli's equation, which is an energy conservation law. If the outlet of the firehose pipe remains closed then there will be only pressure (also called pressure head) of the water. This pressure will provide the kinetic energy to the water when it will be released to a target and there will be additional atmospheric pressure also. So

the pressure inside the pipe = atmospheric pressure + kinetic energy

and the kinetic energy = the potential energy i.e. height*density of water* 9.8

the density of water = 1000 kg/m³

atmospheric pressure = 1.013x10⁵ Pa

so, pressure P= 1.013x10⁵ + 38*1000*9.8

= 1.013x10⁵ +3.724x10⁵

= 4.74x10⁵ (in Pa)