Question

You're in a car that gets 37 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:

Required diameter of hose pipe = 0.2864 mm

Solution:

From the continuity eqn, the fluid flow rate is given by:

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

where

A = cross-sectional area = $\pi r^{2}$

r = hose pipe radius

v = velocity of gas

Also, $v = \frac{displacement, d}{time, t}$

Using:

1 gallon = 3.854 l

1 mile = 1609.34 m

$1 m^{3} = 1000 l$

Therefore,

$A\frac{d}{t} = \frac{V}{t}$

$\pi r^{2} = \frac{V}{d}$

$\pi r^{2} = \frac{(1 gal).(\frac{3.7854 l}{gal}).(\frac{10^{- 3} m^{3}}{l})}{37 miles(\frac{1609.34 m}{miles})}$

$6.357\times 10^{- 8} = \pi r^{2}$

$r^{2} = 2.024\times 10^{- 8}$

$r = 1.423\times 10^{- 4} m = 0.1423 mm$

The diameter of the hose pipe = 2r = $2\times 1.423\times 10^{- 4}$

The diameter of the hose pipe = $2.846\times 10^{- 4} m = 0.2846 mm$