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Chapter 5: Problem 13

At cruise conditions, air flows into a jet engine at a steady rate of 65 lbm/s. Fuel enters the engine at a sieady rate of \(0.60 \mathrm{Ism} / \mathrm{s}\). The average velocity of the exhaust gases is 1500 ft/s relative to the engine. If the engine exhaust effective cross-sectional area is \(3.5 \mathrm{ft}^{2}\), estimate the density of the exhaust gases in \(\mathrm{lbm} / \mathrm{ft}^{3}\).

Short Answer

Expert verified
The estimated density of the exhaust gases is \(0.0125 lbm/ft^3\)

Step by step solution

01

Calculate the Total Mass Flow Rate Out of the Engine

Firstly, calculate the total mass flow rate out of the jet engine by using the conservation of mass principle, which states that the total mass flow rate of air and fuel entering the engine must be equal to the mass flow rate of the exhaust gases exiting the engine. Given that air flows into the engine at a rate of 65 lbm/s and fuel at a rate of 0.60 lbm/s, the total incoming mass flow rate is \(65 lbm/s + 0.60 lbm/s = 65.60 lbm/s\)
02

Calculate the Volume Flow Rate of the Exhaust Gases

The volume flow rate of the exhaust gases can be obtained from the product of the cross-sectional area of the exhaust and the velocity of the gases. So, \(Volume Flow Rate = Area*Velocity = 3.5ft^2 * 1500 ft/s = 5250 ft^3/s\).
03

Find the Density of the Exhaust Gases

The density of the exhaust gases can be found by dividing the mass flow rate by the volume flow rate. Therefore, the density of the exhaust gases is \(Density = Mass Flow rate / Volume Flow Rate = 65.60 lbm/s / 5250ft^3/s = 0.0125 lbm/ft^3\)

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