Question

You're in a car that gets 28 miles per gallon of gas, driving it at a constant speed. If you took the gas from the car tank, and instead filled a long cylinder or hose alongside the car's path, what would the diameter of the hose need to be?

Answer 1

Answer:

The diameter of the hose is 0.326 mm.

Explanation:

Given that,

Speed of car = 28 miles/galllon

We need to calculate the radius

The rate of flow of fluid is from the equation of continuity

$\dfrac{V}{t}=Av$

Where, A = area of cross sectional

$\dfrac{V}{t}=\pi r^2v$

We know that,

The velocity is the ratio of displacement of gas per unit time.

$\dfrac{V}{t}=\pi r^\dfrac{x}{t}$

$\dfrac{V}{x}=\pi r^2$

Put the value into the formula

$\dfrac{0.00378541}{28\times1609.34}=\pi r^2$

$r=\sqrt{\dfrac{0.00378541}{28\times1609.34\times\pi}}$

$r=1.63\times10^{-4}\ m$

We need to calculate the diameter of the hose

$d = 2r$

Put the value of r

$d=2\times1.63\times10^{-4}$

$d=0.326\ mm$

Hence, The diameter of the hose is 0.326 mm.