Before Fuel Injection. Some automobile engines (mainly older ones) use a carbure

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 6.1 cm, with velocity v = 7.1 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 = 38 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.

I really want to learn how to do this problem and also future problems similar to this one, so please show all of your work. In other words, show step by step how you arrived at the answer(s). Include any equations or formulas used to arrive at the answer(s). Thanks!

Explanation / Answer

Here,

v = 7.1 m/s

d1 = 6.1 cm

r1 = 3.05 cm

Now , for the pressure difference

P = p * g * h

P = 1000 * 9.8 * 0.38

P = 3724 Pa

let the velocity of air at d2 is v2

Using Bernoulli's equation

P = 0.5 * p * (v2^2 - v^2)

3724 = 0.5 * 1.29 * (v2^2 - 7.1^2)

solving for v2

v2 = 76.3 m/s

Now , for the diameter d2

using continuity equation

A1 * v = A2 * v2

pi * (6.1)^2 * 7.1 = pi * (d2)^2 * 76.3

solving for d2

d2 = 1.86 cm

the diameter of the d2 is 1.86 cm

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