1. A water tank is 10 m in diameter and the normal depth is 8 m. The outlet is a short 3-inch internal diameter horizontal pipe at the bottom.

(a) What is the initial flow rate of water from the tank? (Neglect friction loss in the pipe).

(b) How long will it take for the tank to be half empty?

(c) What is the average flow rate during that process?

(d) When the tank is half empty, a feed to the tank with a flowrate of 0.08 m^3/s is started, without stopping the outlet flow. How long will it take to refill the tank to the normal height of 10 m?

2. A system consists of superheated steam at 1.0 MPa and 250 C. The steam then slowly expands isentropically until it reaches a final pressure of 100 kPa. Assume that heat can flow into or out of the system to ensure the process is isentropic, but the amount of material in the system is constant. What is the enthalpy of the system (per kg of material) at the conclusion of the expansion?

3. Calculate the fugacity of n-butane at 400 K and at a molar volume of 435 cm^3/mol assuming that n-butane can be described with the van der Waals equation of state.