Question

Assume it takes 8.00 min to fill a 50.0-gal gasoline tank. (1 U.S. gal = 231 in.3) (a) Calculate the rate at which the tank is filled in gallons per second. .104 Correct: Your answer is correct. gal/s (b) Calculate the rate at which the tank is filled in cubic meters per second.

Answer 1

The volumetric rate or flow rate of a fluid is defined as the amount of the volume of a fluid circulating on a surface per unit of time. In this case we have units given initially: Gallons and minutes. For the first part we will convert the minutes to seconds, and we will obtain the flow rate under that measure. For the second case we will convert the gallons to cubic meters and obtain the desired value. Recall the following conversion rates,

$1 min = 60s$

$1 U.S Gal = 0.00378541178 m^3$

If the flow rate is defined as the volume by time, the flow rate with the given values is

$Q = \frac{V}{t}$

$Q = \frac{50Gal}{8min}$

$Q = 6.25 Gal/min$

PART A ) Converting to Gal/seconds, we have,

$Q = 6.25 \frac{Gal}{min}(\frac{1min}{60s})$

$Q = 0.10416Gal/s$

PART B) Converting Gal/seconds to $m^3/s$

$Q = 0.104116\frac{Gal}{s} (\frac{0.00378541178 m^3}{1 Gal})$

$Q = 3.941*10^{-4}m^3/s$