Consider a firefighter who is standing on a ladder and spraying water with a hose into Chief Inspector Jacques Clouseau’s (Figure 3a) third-story apartment. A diagram of the hose/nozzle used by the firefighter is shown in Figure 3b. Assume the nozzle has little effect on the flow in the hose and water in the hose/nozzle is incompressible. The temperature of the water in the hose is 15 ◦C. Part 1: Analysis of the flow through the fire hose nozzle (Hint: Use the integral form of the conservation equations). (a) Write down the general mass conservation equation for an arbitrary control volume. (b) Choose an appropriate control volume for the fire hose nozzle and deduce the simplest form of the steady-state mass conservation equation for the nozzle. (c) Write down the general momentum conservation equation for an arbitrary control volume. (d) Assuming that the flow is inviscid, calculate the gage pressure in the hose. Hint: Consider an energy conservation equation. (e) Calculate the force with which the nozzle acts on the water. Show its direction in a simple schematic of the hose/nozzle system. Part 2: Analysis of losses in the hose. (f) What is the Reynolds number of the flow in the hose? (g) If the relative surface roughness of the hose is 0.01 and the hose is 15 m long, what head loss must a pump in the fire truck overcome to achieve the described flow rate? Neglect minor losses.
Consider a firefighter who is standing on a ladder and spraying water with a hose into Chief Inspector
Jacques Clouseau’s (Figure 3a) third-story apartment. A diagram of the hose/nozzle used by the
firefighter is shown in Figure 3b. Assume the nozzle has little effect on the flow in the hose and water
in the hose/nozzle is incompressible. The temperature of the water in the hose is 15 ◦C.
Part 1: Analysis of the flow through the fire hose nozzle (Hint: Use the integral form of the
conservation equations).
(a) Write down the general mass conservation equation for an arbitrary control volume.
(b) Choose an appropriate control volume for the fire hose nozzle and deduce the simplest form of
the steady-state mass conservation equation for the nozzle.
(c) Write down the general momentum conservation equation for an arbitrary control volume.
(d) Assuming that the flow is inviscid, calculate the gage pressure in the hose. Hint: Consider an
energy conservation equation.
(e) Calculate the force with which the nozzle acts on the water. Show its direction in a simple
schematic of the hose/nozzle system.
Part 2: Analysis of losses in the hose.
(f) What is the Reynolds number of the flow in the hose?
(g) If the relative surface roughness of the hose is 0.01 and the hose is 15 m long, what head loss
must a pump in the fire truck overcome to achieve the described flow rate? Neglect minor losses.
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