+ (a) A tank contains 100 liters of saltwater with 5 kg of dissolved salt. Freshwater enters the tank at a rate of 4 liters per minute, and the well-mixed solution leaves the tank at the same rate. Let y(t) represent the amount of salt (in kg) in the tank at time t (in minutes). Set up and solve a differential equation to find y(t). [Hint: The inflow rate of fresh water equals to the outflow rate of the well-mixed solution, so the total volume of the saltwater in the tank (100 liters) remains constant over time. At any time (t), the salt content (concentration) in the tank is y(t) (kg/liter)] 100 (b) How much time does it take for the salt content to decrease by 50%. [Note: Write down the numerical expression, no need to use calculator]

2. Freshwater and saltwater flowing in parallel horizontal pipelines are connected to each other by a double U-tube manometer. Determine the pressure difference between the two pipelines. Take the density of seawater at that location to be p kg = 1035 m3 · - Air Fresh- water 40 cm Sea- water 70 cm 60 cm 10 cm -Mercury

Use the following given values to solve problems, unless otherwise stated. Ywater = 9790 N/m³ = 62.4 lbf/ft°; g = 9.81 m/s? = 32.2 ft/s²; 1 hp = 550 lbf-ft/s = 746 Watts Problem-1 Water is pumped from the large tank through a uniform diameter pipe (d = 3 in.) and exits as a free jet (refer figure-a). The plot of the flowrate (Q) versus pump-head (hp) is a straight-line graph that passes through points (3, 16) as shown in figure-b. If the pipe friction head loss is, hf = 7V:/2g, where V is the average fluid velocity in the pipe, find a) the equation that relates hp and Q; b) flowrate and c) If the pump is 75% efficient, what horsepower is needed to drive it? Assume steady, incompressible flow. Ignore kinetic energy correction factor (a). 12 ft Pump %3D (a) 16 3. Q, ft°ls (b) dy