Question

A mechanical pump is used to pressurize a bicycle tire. The inflow to the pump is 0.6 cfm. The density of the air entering the pump is 0.075 lbm/ft3. The inflated volume of a bicycle tire is 0.040 ft3. The density of air in the inflated tire is 0.4 lbm/ft3. How many seconds does it take to pressurize the tire if there initially was no air in the tire?

Answer 1

The time it takes to pressurize the tire is approximately 1.25 seconds.

Step-by-step explanation:

To calculate the time it takes to pressurize the tire, we can use the equation:

Time = Volume / Flow Rate

Given that the tire's inflated volume is 0.040 ft3 and the inflow to the pump is 0.6 cfm, we can convert the units to match:

0.6 cfm x (1 ft3 / 7.48 gal) x (1 gal / 3.785 L) x (1 L / 1000 cm3) = 0.032 ft3/s

Now we can calculate the time:

Time = 0.040 ft3 / 0.032 ft3/s = 1.25 s

Therefore, it will take approximately 1.25 seconds to pressurize the tire.

Answer 2

0.75 seconds

Step-by-step explanation:

Given information

Inflow=0.6 cfm

Density of air entering= 0.075 lbm/ft3

Bicycle’s inflated volume= 0.040 ft3

density of air in the inflated tire= 0.4 lbm/ft3

Mass of air pumped=density*volume=0.075*0.04=0.003 lbm

This mass of air pumped is same as mass of air in the inflated tire

Volume of inflated tire=mass/density=0.003/0.4=0.0075 ft3

Time=0.0075/0.6= 0.0125 mins

0.0125*60=0.75 seconds