Question 1. A Continuous miner has two 74.6 kW, 660V, and 3,600 rpm three phase squirrel cage induction motors. Calculate the current drawn from the line and total power factors when:

a) The first motor is being started
b) The second motor is being started and the first motor is running at full speed
c) Both motors are started simultaneously
d) Both motors are running at full speed
The motors have a power factor of 80% lagging at normal full speed and 30% lagging at the time of starting. Assume the motors are started directly on line with full load.

Question 2. A three-phase 660V alternating current substation supplies power to the following loads: (a) 90 kVA at 85% lagging power factor, and (b) 29kW at 100% power factor. Determine the operating power factor of the substation. In this case a 50kW synchronous motor is to be installed at the substation to improve the station power factor to 95% lagging. Determine the power factor at which the synchronous motor must operate to achieve this.

Question 3. A 100 kW, 450V AC shuttle car uses a flat cable. Two layers of the cable will remain on the shuttle car's reel at all times. What is the required ampacity for the cable if efficiency is 80%, a power factor of unity also applies.

Question 4. A long wall section has the following equipment.

Load factors for all the motors can be assumed to be 0.8 except the pump packs, these have a load factor of 0.9. Determine the current supplied to the high side of the load centres transformer. The distribution voltage is 6,600 V. (Hint: When motor power factors are unknown, assume that they are equal to the load factors (up to about 0.85)

Question 5. A confined sand aquifer has an effective porosity of 35% and a hydraulic conductivity of 30 m/day. The hydraulic gradient in the aquifer is 0.02 The overlying confining bed is composed of clay with a porosity of 45% and a hydraulic conductivity of 0.0002 m/day. Hydraulic gradient in the clay is 0.15. Determine the specific discharge and seepage (average linear) velocity for flow of ground water in both the aquifer and the overlying aquitard.

Question 6. Field investigations indicate that the hydraulic gradient in a 20m thick sand aquifer is 0.01. The transmissivity of the aquifer has been determined from pumping tests to be 500 m2/day:. The porosity of the sand is 0.25. Calculate the discharge and linear velocity.

Question 7. The hydraulic gradient measured in two observation bores positioned along the direction of groundwater flow in a 30m thick confined aquifer is 0.001; the aquifer's transmissivity is 750 m2/day. Determine the groundwater flow through a 6 km wide section in the direction of groundwater flow.

Question 8. An unconfined aquifer is 33 m thick and 7 km wide. Two observation bores are located 1.2 km apart in the direction of flow. The head in bore 1 is 97.5 m and in bore 2, it is 89m. Hydraulic conductivity is 1.2 m/day.
a) What is the total daily flow of water through the aquifer
b) What is the elevation of the potentiometric surface at a point located 0.2 km from bore 1 and 1 km from bore 2