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Chapter 1: Problem 23

Water flows from a large drainage pipe at a rate of 1200 gal/min. What is this volume rate of flow in (a) \(m^{3} / s\) (b) liters / \(\min ,\) and (c) \(\mathrm{ft}^{3} / \mathrm{s} ?\).

Short Answer

Expert verified
The volume rate of flow is approximately 0.754 \(m^{3} / s\), 4536.49 liters / \(\min\), and 2.674 \(\mathrm{ft}^{3} / \mathrm{s}\).

Step by step solution

01

Converting to Cubic Meters per Second

First, convert the volume rate of flow from gallons per minute to cubic meters per second. One gallon is approximately 0.00378541 cubic meters, and one minute has 60 seconds. Therefore, the rate of 1200 gal/min can be converted as follows: \(1200 \, \text{gal/min} * 0.00378541 \, m^{3}/\text{gal} * 1/60 \, \text{min/s} = 0.7539876 \, m^{3}/s.\)
02

Converting to Liters per Minute

Next, convert the unit to liters per minute. One gallon is approximately 3.78541 liters. Therefore, we have \(1200 \, \text{gal/min} * 3.78541 \, \text{liters/gal} = 4536.49 \, \text{liters/min}.\)
03

Converting to Cubic Feet per Second

Finally, convert the flow rate to cubic feet per second. One gallon is approximately 0.133681 cubic feet, and again, one minute has 60 seconds. Therefore, the conversion is: \(1200 \, \text{gal/min} * 0.133681 \, \text{ft^{3}/gal} * 1/60 \, \text{min/s} = 2.67362 \, \text{ft^{3}/s}\).

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Most popular questions from this chapter

The force, \(F\), of the wind blowing against a building is given by \(F=C_{D} \rho V^{2} A / 2,\) where \(V\) is the wind speed, \(\rho\) the density of the air, \(A\) the cross-sectional area cf the building, and \(C_{D}\) is a constant termed the drag coefficient. Determine the dimensions of the drag coefficient.

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