For the following calculations, take g = 9.8m/s2 and Pwater=1000kg/m^3
1. Assuming there are both a pressure gage and a manometer attached to a gas tank which has a pressure lower than Patm. If the reading on the pressure gage is 10kPa and atmospheric pressure is 100kPa, determine (a) the absolute pressure of the tank, and (b) the height of the fluid between the two fluid levels in the manometer, given the fluid is has a specific gravity of 1.5.
2. Calculate (a) the energy of a 1150-kg car consumes if it is driving at a velocity of 20m/s and a 100 m-long uphill road with a slope of 10°; (b) the power is will require if the car is accelerating from 2m/s to 10m/s in 0.5s on a flat road. Disregard friction, air drag, and rolling resistance.
3. Considering a river flowing toward a lake which is 40 m below. It is known that the river flows at a constant velocity of 5 m/s at a rate of 3 m3/s. Ignoring the flow energy, please determine: (a) the total specific mechanical energy of the river water; (b) the maximum power it can generate of the river at that location.
4. A fan is to accelerate quiescent (velocity is 0 m/s) air to a velocity of 10m/s at a rate of 3 m3/s. If the density of air is 1.15 kg/m3, determine the minimum electric power that must be supplied to the fan.
5. An oil pump is powered by a 5kW electric motor. The pressure at the outlet and the inlet of the pump at full load is measured to be 450 kPa and 200kPa, respectively. If the oil flow rate through the pump is 18L/s and the changes in elevation and the flow velocity across the pump are negligible. Determine 1) the energy flow rate of the oil at the inlet; 2) the difference of energy flow rate between the outlet and inlet; 3) the overall efficiency of the motor-pump system?
6. To generate electricity, a hydraulic turbine-generator system is installed at a lake location where the depth of the water is 50 m. Neglecting the kinetic and flow energy, if water is to be supplied at a rate of 5000 kg/s, the shaft power generated is measured to be 2000 kW, and the overall efficiency is 75 percent, determine (a) the mechanical efficiency of the turbine; (b) the electrical efficiency of the generator; (c) the electrical power generated; (d) the electrical current if the output voltage of the generator is 1200V; (e) the shaft rotation rate (in rpm) if the torque is 20N.m.