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Chapter 8: Problem 116

A 250 ft-high building has a 6.065 -in.-diamcter steel standpipe and a 100 -ft-long \(2 \frac{9}{16}\) -in. diameter fire hose on each floor. The nearest fireplag is \(100 \mathrm{ft}\) from the standpipe's ground-level connection. Assume that fire-fighters connect a 6 -in.- -diameter, 50 -ft-long fire hose from the fireplug to the fire truck and a 4-in.- -diameter. 50-ft-long fire hose from the fire truck to the standpipe's groundlevel connection. The National Fire Protection Association (NFPA) requires that a minimum pressure of 65 psig be meintained at the connection of the \(2 \frac{9}{16}\) -in.- -diameter hose and the standpipe while maintaining a flow rate of 500 gal/min through the fire hose. What pressure rise must the pump on the fire engine supply to satisfy the NFPA requirement for this building? The fire hydrant water pressure is 80 psiz and the water temperature is \(60^{\circ} \mathrm{F}\). The connections are threaded.

Short Answer

Expert verified
To find the pressure rise that the pump must supply, calculate the total head loss in the system and add it to the pressure required at the hose connection. The calculated value is the necessary pressure rise.

Step by step solution

01

Identify known and unknown quantities

Identify all known quantities such as hose lengths, their diameters, pressure at the hose connection and the flow rate. The unknown quantity is the pressure rise that the pump must supply.
02

Convert units

To facilitate calculations, convert all quantities into SI units. For example, convert lengths from feet to meters, diameters from inches to meters, pressure from psi to Pascals, and flow rate from gallons per minute to cubic meters per second.
03

Apply Bernoulli’s equation

Bernoulli’s equation (\[p_1 + \frac{1}{2}\rho v_1^2 + \rho gh_1 = p_2 + \frac{1}{2}\rho v_2^2 + \rho gh_2)\] is used to relate the quantities at the two ends of the pipes. Here, \(\rho\) is fluid density, \(v\) is fluid velocity, \(g\) is acceleration due to gravity, \(h\) is height, and \(p\) is pressure.
04

Compute velocity

Using the relationship between flow rate (\(Q\)) and velocity (\(v\)), and cross-sectional area, the velocity in each pipe section can be calculated. This will be helpful in calculating the total head loss.
05

Use Darcy-Weisbach equation for head loss

The Darcy-Weisbach equation (\[h_f = f \frac{L}{D} \frac{v^2}{2g}\]), where \(h_f\) is head loss, \(f\) is friction factor, \(L\) is length of pipe, \(D\) is diameter of pipe, \(v\) is fluid velocity, is used to calculate head loss in each pipe.
06

Calculate total head loss and pump pressure

The total head loss in the system is computed as the sum of the head losses in each piece of equipment (standpipe, hoses). The pump pressure is found by adding this total head loss to the pressure required at the hose connection.

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Most popular questions from this chapter

The Churchill formula for the friction factor is $$f=8\left[\left(\frac{8}{\mathrm{Re}}\right)^{12}+\frac{1}{(A+B)^{15}}\right]^{1 / 12}$$ where $$\begin{array}{l} A=\left\\{-2.457 \ln \left[\left(\frac{7}{\mathrm{Re}}\right)^{0.9}+\frac{\varepsilon}{3.7 D}\right]\right\\}^{16} \\ B=\left(\frac{37.530}{\mathrm{Re}}\right)^{16} \end{array}$$ Compare this equation for \(f\) for both the laminar and turbulent regimes for \(\varepsilon / D=0.00001,0.0001,0.001,\) and 0.01 and Reynolds numbers of \(10,10^{2}, 10^{3}, 10^{4}, 10^{5}, 10^{6},\) and \(10^{7}\) with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.

For fully developed laminar pipe flow in a circular pipe, the velocity profile is given by \(u(r)=2\left(1-r^{2} / R^{2}\right)\) in \(\mathrm{m} / \mathrm{s},\) where \(R\) is the inner radius of the pipe. Assuming that the pipe diameter is \(4 \mathrm{cm},\) find the maximum and average velocities in the pipe as well as the volume flow rate.

Carbon dioxide at a temperature of \(0^{\circ} \mathrm{C}\) and a pressure of \(600 \mathrm{kPa}(\text { abs })\) flows through a horizontal \(40-\mathrm{mm}\) -diameter pipe with an average velocity of \(2 \mathrm{m} / \mathrm{s}\). Determine the friction factor if the pressure drop is \(235 \mathrm{N} / \mathrm{m}^{2}\) per 10 -m length of p pe.

A certain process requires 2.3 cfs of water to be delivered at a pressure of 30 psi. This water comes from a large-diameter supply main in which the pressure remains at 60 psi. If the galvanized iron pipe connecting the two locations is 200 ft long and contains six threaded \(90^{\circ}\) elbows, determine the pipe diameter. Elevation differences are negligible.

{ Blood iassume } \mu=4.5 \times 10^{-5} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}, S G=1.0\right)\( flows through an artery in the neck of a giraffe from its heart to its head at a rate of \)2.5 \times 10^{-4} \mathrm{ft}^{3} / \mathrm{s}\(. Assume the length is \)10 \mathrm{ft}\( and the diameter is 0.20 in. If the pressure at the beginning of the artery (outlet of the heart) is equivalent to \)0.70 \mathrm{ft}$ Hg, determine the pressure at the end of the artery when the head is (a) 8 ft above the heart, or (b) 6 ft below the heart. Assume steady flow. How much of this pressure difference is due to elevation effects, and how much is due to frictional effects?
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