Question

It takes you 1 min to fill your car's fuel tank with 8.8 gallons of gasoline. What is the approximate average velocity of the gasoline leaving the 0.60-in.-diameter nozzle at this pump

Answer 1

To find the average velocity of gasoline exiting a pump nozzle, convert the flow rate from gallons per minute to cubic centimeters per second, find the cross-sectional area of the nozzle, and then divide the flow rate by the area. The calculated average velocity for an 0.60-inch-diameter nozzle with a flow rate of 8.8 gallons per minute is approximately 286.85 cm/s.

Step-by-step explanation:

To find the average velocity of gasoline exiting the nozzle, we need to consider the flow rate and the cross-sectional area of the nozzle. The flow rate is given as 8.8 gallons per minute, which we can convert to cubic centimeters per second (cm³/s) since velocity will be in cm/s.

First, we convert gallons to liters and then to cubic centimeters:

• 1 gallon = 3.78541 liters
• 1 liter = 1000 cm³

So, 8.8 gallons/min converts to:

(8.8 gallons) * (3.78541 liters/1 gallon) * (1000 cm³/1 liter) * (1 min/60 seconds) = 522.6 cm³/s

Next, we calculate the cross-sectional area (A) of the nozzle:

• diameter (d) = 0.60 inches
• Radius (r) = d/2 = 0.30 inches

First, we convert inches to centimeters since we are looking for velocity in cm/s:

(0.30 inches) * (2.54 cm/1 inch) = 0.762 cm

Now, find the area using the formula for the area of a circle, A = πr²:

A = π * (0.762 cm)² = 1.822 cm²

Finally, we calculate the velocity (v) using the flow rate (Q) and the cross-sectional area (A), so:

v = Q/A = 522.6 cm³/s / 1.822 cm² = 286.85 cm/s

Therefore, the average velocity of gasoline leaving the 0.60-inch-diameter nozzle is approximately 286.85 cm/s.

Answer 2

v = 119 in/s

Step-by-step explanation:

Given,

time to fill car's fuel = 1 min = 60 s

Fuel in the tank after 1 min = 8.8 gallons

diameter of pipe = 0.60 in

average velocity of the gasoline = ?

Now,

Discharge(Q) =
`(8.8 * 231\ in^3)/(60\ s)`

=
`33.88\ in^3/ft`

We know that

Q = Av

`v = (Q)/(A)`

`v = (33.88)/((\pi)/(4)* d^2)`

`v = (33.88)/((\pi)/(4)* 0.6^2)`

v = 119 in/s

Average velocity of gasoline is equal to 119 in/s.