Question

1. a sump pump is stated to have a flow rate of 2500 gallons per hour. what is that flow rate in cubic centimeters per second? (1 gal = 0.134 ft³)

Explanation:

Step1: Convert gallons per hour to cubic feet per hour

Given the flow rate is 2500 gallons per hour and \(1\) gal \( = 0.134\) ft³. So we multiply the flow rate in gallons per hour by the conversion factor to get cubic feet per hour.
\(2500\space\frac{\text{gal}}{\text{h}}\times0.134\space\frac{\text{ft}^3}{\text{gal}} = 335\space\frac{\text{ft}^3}{\text{h}}\)

Step2: Convert cubic feet per hour to cubic feet per second

There are 3600 seconds in an hour. So we divide the flow rate in cubic feet per hour by 3600 to get cubic feet per second.
\(335\space\frac{\text{ft}^3}{\text{h}}\div3600\space\frac{\text{s}}{\text{h}}=\frac{335}{3600}\space\frac{\text{ft}^3}{\text{s}}\approx0.09306\space\frac{\text{ft}^3}{\text{s}}\)

Step3: Convert cubic feet to cubic centimeters

We know that \(1\) ft \( = 30.48\) cm, so \(1\) ft³ \(=(30.48\space\text{cm})^3 = 30.48^3\space\text{cm}^3\approx28316.85\space\text{cm}^3\). Now we multiply the flow rate in cubic feet per second by the conversion factor to get cubic centimeters per second.
\(0.09306\space\frac{\text{ft}^3}{\text{s}}\times28316.85\space\frac{\text{cm}^3}{\text{ft}^3}\approx2635\space\frac{\text{cm}^3}{\text{s}}\)

Answer:

\(\approx 2635\space\frac{\text{cubic centimeters}}{\text{second}}\) (or more precisely, following the calculation steps, the value is approximately 2635 \( \text{cm}^3/\text{s} \))