Methane, with a density of 0.52 kg/m3, enters a burner with a velocity of 30 m/s through a cross-sectional area of 8.2 cm2. Air, with a density of 1.20 kg/m3, enters at a mass flow rate 21 times that of the methane. Exhaust gas, with a flow density of 0.68 kg/m3; leaves through a cross-sectional area of 196 cm2. If the flow is steady, determine the exhaust velocity.

A t-joint is another common piping component, typically used to combine or separate flows of fluid. This t-joint has two inlets and one outlet. We want to find the flow rate through the outlet and the force to hold the t-joint in place. The working fluid is water. One inlet, open to the left, is 6 cm diameter and receives water at a velocity of 4 ms ¹. The other inlet, open to the right, has a volume flow rate of 1 Ls¹ and a diameter of 4 cm. If the outlet has a diameter of 12 cm and faces upwards with regard to gravity, determine: (a) the velocity through the second inlet. [0.80 m s-¹] (b) the velocity through the outlet. [1.09 m s-¹] (c) the reaction forces (x, y directions) to hold the t-joint in place [x: -181.7 N, y: 1156 N] Losses due to viscosity are assumed negligible. The outlet discharges to atmosphere. The weight of the t-joint and the fluid within it are negligible.

1) Air with a density of 0.45 kg/m3 enters an experimental jet engine at a rate of 175 m/s. The inlet area of the engine is 7.0 ft2. After fuel is burned, the air and combustion byproducts leave the engine with a velocity of 695 m/s through an outlet area of 6.0 ft2. What is the average density of the gas exiting the engine? Express your answer in kg/m3, slugs/ft3, and lbm/ft3. 2)  Calculate the mass moment of inertia of the thin ring shown in the accompanying diagram. Express your answer in lbm · ft2, lbm · in2, and slugs · ft2. (Assume the axis of rotation is into the page through the center of the ring.) m = 0.8 slugs radius is 9 in.