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Chapter 4: Problem 74

Water flows steadily through a fire hose and nozzle. The hose is \(75 \mathrm{mm}\) inside diameter, and the nozzle tip is \(25 \mathrm{mm}\) ID; water gage pressure in the hose is \(510 \mathrm{kPa}\), and the stream leaving the nozzle is uniform. The exit speed and pressure are \(32 \mathrm{m} / \mathrm{s}\) and atmospheric, respectively. Find the force transmitted by the coupling between the nozzle and hose. Indicate whether the coupling is in tension or compression.

Short Answer

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Use the short answer field to input the calculated force and the nature of the force i.e., tension or compression.

Step by step solution

01

Determine the mass flow rate

The mass flow rate can be calculated using the formula for flow speed, cross-sectional area of the pipe, and water density. Because the flow is steady, the mass flow rate is the same at every cross-section of the hose and nozzle. The formula for flow rate is \( \dot{m} = 蟻 * A * v \), where 蟻 is the density of the water (1000 kg/m鲁), A is the cross-sectional area of the hose which is \( 蟺*(d^2)/4 \) and v is the velocity of water. Here, the diameter d of the hose is 75mm or 0.075m, and the velocity v is not given for this section of the hose but will be the same as at the exit (32 m/s). By substituting these values, compute for mass flow rate.
02

Compute for exit pressure

The exit pressure is provided as being atmospheric, which is equal to zero gauge pressure.
03

Apply momentum equation

The linear momentum equation is given by \( 危F = \dot{m}*(V_{out} - V_{in}) \), which is the sum of all forces equal to the change in momentum. Since fluid enters the control volume with negligible velocity as compared to the exit velocity, the equation simplifies to \( 危F = \dot{m}*V_{out} \). Here, 危F is the vector sum of external forces acting on the control volume, \(\dot{m}\) is the mass flow rate, \(V_{out}\) is the exit speed, and \(V_{in}\) is the inlet speed. By plugging in the known values, compute for 危F.
04

Determine the nature of the force

If the force computed is positive, the coupling is in tension. If the force is negative, it signifies that the force is acting in the opposite direction, thereby implying that the coupling is in compression.

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Most popular questions from this chapter

A block of copper of mass 5 kg is heated to \(90^{\circ} \mathrm{C}\) and then plunged into an insulated container containing 4 L of water at \(10^{\circ} \mathrm{C}\). Find the final temperature of the system. For copper, the specific heat is \(385 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K},\) and for water the specific heat is \(4186 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\).

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