Question

A simple jet carburetor is required to supply 5 kg of air and 0.5 kg of fuel per minute. The fuel specific gravity is 0.75. The air is initially at 1 bar and 300 K. Calculate the throat diameter of the venturi when the velocity at throat is 100 m/s. The velocity discharge coefficient for air is 0.8. If the pressure drop across the fuel metering orifice is 80% of the pressure drop from inlet to throat of the venturi, calculate the orifice diameter assuming Cdf=0.6 and =1.4.

Answer 1

To calculate the throat diameter of the venturi, we first need to find the mass flow rate of the air. The throat diameter of the venturi is approximately 2.64 cm. To calculate the orifice diameter, we first need to find the pressure drop from inlet to throat of the venturi.

Step-by-step explanation:

To calculate the throat diameter of the venturi, we first need to find the mass flow rate of the air. The mass flow rate of the air is given by:

Mass flow rate of air = mass of air per minute = 5 kg/minute

Next, we can find the velocity of the air at the throat of the venturi using the velocity discharge coefficient:

Velocity at throat = velocity discharge coefficient * velocity at inlet = 0.8 * 100 m/s = 80 m/s

Using the equation of continuity, we can relate the throat diameter, velocity at throat, and mass flow rate:

Throat diameter = (4 * mass flow rate) / (density * velocity at throat * π)

Substituting the given values, we have:

Throat diameter = (4 * 5 kg/minute) / (1.18 kg/m^3 * 80 m/s * π) = 0.0264 m = 2.64 cm

So, the throat diameter of the venturi is approximately 2.64 cm.

To calculate the orifice diameter, we first need to find the pressure drop from inlet to throat of the venturi. The pressure drop from inlet to throat can be calculated using Bernoulli's equation:

Pressure drop from inlet to throat = (1/2) * density * (velocity at throat)^2 = (1/2) * 1.18 kg/m^3 * (80 m/s)^2

The pressure drop across the fuel metering orifice is given as 80% of the pressure drop from inlet to throat:

Pressure drop across fuel metering orifice = 0.8 * Pressure drop from inlet to throat

Next, we can use the pressure drop across the fuel metering orifice to find the orifice diameter using the following equation:

Orifice diameter = √((4 * mass flow rate * (viscosity fuel * pressure drop across fuel metering orifice)) / (pressure * (orifice discharge coefficient) * π))

Substituting the given values, we have:

Orifice diameter = √((4 * 0.5 kg/minute * (0.75 * 0.8 * Pressure drop from inlet to throat)) / (1 bar * 1.4 * π))

Since the pressure is given in bar, we need to convert it to N/m^2:

1 bar = 100,000 N/m^2

Substituting the value of Pressure drop from inlet to throat, we can calculate the orifice diameter.