Question

Fire hoses used in major structure fires have inside diameters of 2.500 in (1 in = 2.54 cm). The nozzle of the fire hose have an inside diameter of 1.200 in. When firefighters are fighting a fire 2020.007 cm above the ground, the pressure in the nozzle is less than at ground level. When measured, the gauge pressure in the nozzle is 0.000 Pa.

(a) How are the firefighters able to fight a fire with zero water pressure? Explain your answer.

(b) What is the value of the water pressure as it emerges into the air from the nozzle? Explain your answer

Answer 1

Consider the following situation:

Now, appl Bernoulli's equation by considering the given data. Even we can make a good estimate based on our theoretical assumptions and later we will try to put some values given if required. So, here we go -

Actually, the pressure in the nozzle of this fire hose is less than at ground level for two reasons: the water has to go uphill to get to the nozzle, and speed increases in the nozzle. In spite of its lowered pressure, the water can exert a large force on anything it strikes, by virtue of its kinetic energy. Pressure in the water stream becomes equal to atmospheric pressure once it emerges into the air without any sort of significant change in initial conditions. And that's how they are able to get water from nozzle at very high velocity and very - very low pressure as compared to the pressure and velocity generated by pump in the hose just before the nozzle. Now, to get more satisfactory feeling about this analysis, you can put some values of initial pressure, find velocities from continuity equation by using a suitable flow rate and put in the above equation to find out pressure at the exit of the nozzle. I hope it comes to be very close to zero as said earlier.