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Question 3 A piston compresses gas in a cylinder at constant speed $V = 15 \text{ m/s}$. At one instant when the piston is at $L_0 =$ 0.14 m away from the closed end of the cylinder, the gas density $\rho_0 = 18 \text{ kg/m}^3$. The gas velocity varies linearly from V at the piston to zero at the closed end. Determine (1) an expression for the average gas density as a function of time, and (2) the rate of change of gas density at this instant. Use the continuity equation. Assume the gas in the cylinder is unsteady, uniform, 1-D, and compressible.

          Question 3
A piston compresses gas in a cylinder at constant speed $V = 15 \text{ m/s}$. At one instant when the piston is at $L_0 =$
0.14 m away from the closed end of the cylinder, the gas density $\rho_0 = 18 \text{ kg/m}^3$. The gas velocity varies
linearly from V at the piston to zero at the closed end. Determine (1) an expression for the average gas
density as a function of time, and (2) the rate of change of gas density at this instant. Use the continuity
equation. Assume the gas in the cylinder is unsteady, uniform, 1-D, and compressible.

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Question 3
A piston compresses gas in a cylinder at constant speed V = 15 m/s. At one instant when the piston is at L0 =
0.14 m away from the closed end of the cylinder, the gas density ρ0 = 18 kg/m^3. The gas velocity varies
linearly from V at the piston to zero at the closed end. Determine (1) an expression for the average gas
density as a function of time, and (2) the rate of change of gas density at this instant. Use the continuity
equation. Assume the gas in the cylinder is unsteady, uniform, 1-D, and compressible.

Added by Shane P.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Sri K

10/09/2023

Step 1

This means that the piston's position, L(t), can be expressed as: L(t) = Lo - Vt where Lo is the initial position of the piston and t is time. Show more…

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zcm Question 3 A piston compresses gas in a cylinder at constant speed V = 15 m/s. At one instant when the piston is at Lo = 0.14 m away from the closed end of the cylinder, the gas density Po = 18 kg/m³. The gas velocity varies linearly from V at the piston to zero at the closed end. Determine (1) an expression for the average gas density as a function of time, and (2) the rate of change of gas density at this instant. Use the continuity equation. Assume the gas in the cylinder is unsteady, uniform, 1-D, and compressible. V = constant u(x, 1) p(1) x=0 x = L(t) Formulas

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