Question

Before Fuel Injection. Some automobile engines (mainly older ones) use a carburetor to turn the liquid fuel into vapor and mix it with air for combustion. The basic principle of carburetion is shown in Figure P10.82. A piston moves down in the cylinder thereby moving air from the outside through the carburetor by way of an air filter and into the carburetor. The filtered air enters from the left of Figure P10.82 and moves into the main intake, a tube of diameter 4.2 cm, with velocity v = 10 m/s. The air must pass through a region of the intake that has a smaller diameter. Determine what diameter would be needed cause a change in pressure such that fuel from the reservoir is pulled into the airflow. The surface of the fuel in the reservoir is h = 37 cm below the bottom of the intake and the density of the fuel is 0.45 that of water. Use 1000 kg/m^3 for the density of water and 1.29 kg/m^3 for the density of air

Answer 1

given

diameter 4.2 cm = d₁  

= 0.042 m

with velocity v = 10 m/s

h = 37 cm

= 0.37 m

= 0.45 x 1000 = 450 kg / m³  

P₁ - P₂ = g h

P = 450 x 9.8 x 0.37

P = 1631.7 N/m²    

A₁ V₁ = A₂ V₂  

V₂ = ( d₁ / d₂ )² V₁

using Bernoulli's equation

P₁ + 1/2 _air V₁² + _air g h₁ = P₂ + 1/2 _air V₂² + _air g h₂  

( d₁ / d₂ )² = ( 2 P / _air V₁² ) + 1

= ( 2 x 1631.7 / 1.29 x 10² ) + 1  

( d₁ / d₂ )⁴ = 26.297

d₁ / d₂ = 2.263

d₂ = d₁ / 2.263

= 0.042 / 2.263

d₂ = 0.01855 m

so the needed diameter is d₂ = 1.855 cm