A fuel pump sends gasoline from a car's fuel tank to the engine at a rate of 5.64 10-2 kg/s. the density of the gasoline is 735 kg/m3, and the radius of the fuel line is 3.43 10-3 m. what is the speed at which the gasoline moves through the fuel line?

Given:

Gasoline pumping rate, R = 5.64 x 10⁻² kg/s

Density of gasoline, D = 735 kg/m³

Radius of fuel line, r = 3.43 x 10⁻³ m

Calculate the cross sectional area of the fuel line.

A = πr² = π (3.43 x 10⁻³ m) ² = 3.6961 x 10⁻⁵ m²

Let v = speed of pumping the gasoline, m/s

Then the mass flow rate is

M = AvD = (3.6961 x 10⁻⁵ m²) * (v m/s) * (735 kg/m³) = 0.027166v kg/s

The gasoline pumping rate is given as 5.64 x 10⁻² kg/s, therefore

0.027166v = 0.0564

v = 2.076 m/s

Answer: 2.076 m/s

The gasoline moves through the fuel line at 2.076 m/s.