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Chapter 8: Problem 34

During a heavy rainstorm, water from a parking lot completely fills an 18 -in.-diameter, smooth, concrete storm sewer. If the flowrate is \(10 \mathrm{ft}^{3} / \mathrm{s}\), determine the pressure drop in a \(100-\mathrm{ft}\) horizontal section of the pipe. Repeat the problem if there is a \(2-f t\) change in elevation of the pipe per 100 ft of its length.

Short Answer

Expert verified
For a horizontal pipe, the pressure drop is 3.315 psi. For the pipe with a 2-ft change in elevation per 100-ft length, the total pressure change is 4.795 psi (1.480 psi due to elevation change and 3.315 psi due to velocity change).

Step by step solution

01

Calculate the Velocity

Firstly, determine the cross-sectional area (A) of the pipe using the given diameter (D) by using the formula \(A = π(D/2)^2\), where D is in meters. Since the given diameter is in inches, convert it to feet. Then, calculate the velocity (v) of the water flow using the formula \(v = Q/A\), where Q is the flowrate.
02

Calculate the Pressure Drop for Horizontal Pipe

Now, calculate the pressure drop (∆P) in the 100-ft horizontal section of the pipe using the formula \(\Delta P = 0.5 * \rho * v^2\), where \(\rho\) is the density of water (which is approximately 1000 kg/m^3). The answer will be in Pascals, convert it to psi using the conversion factor 0.0001450377 psi/Pa.
03

Calculate the Pressure Drop for Pipe with Elevation Change

Next, determine the change in pressure due to the change in height. The pressure difference due to a change in fluid column height can be calculated using the formula \(\Delta P = \rho * g * h\), where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the change in elevation of the pipe.
04

Find the Total Pressure Change

Finally, to find the total pressure change for the pipe with elevation change, add the pressure changes calculated in step 2 and step 3.

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Most popular questions from this chapter

Assume a car's exhaust system can be approximated as \(14 \mathrm{ft}\) of 0.125 -ft-diameter cast-iron pipe with the equivalent of six \(90^{\circ}\) flanged elbows and a muffler. (See Video V8.14.) The muffler acts as a resistor with a loss coefficient of \(K_{t}=8.5 .\) Determine the pressure at the beginning of the exhaust system if the flowrate is \(0.10 \mathrm{cfs},\) the temperature is \(250^{\circ} \mathrm{F}\), and the exhaust has the same properties as air.

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