Question

Question 2. A family in Eastern Australia installs solar panels to run an air-source heat pump to heat their swimming pool. The panels produce a total of around 6 kW of electricity during the day. The heat pump draws 5 kW of electricity and delivers 23 kW of heating to the pool.

a) The pool contains 40,000 litres of water. When the heat pump is running, estimate the rate at which the temperature of the water in the pool rises, in kelvins per hour. How much would the pool heat up after 8 hours of running the heat pump? Assume a specific heat capacity for the water of 4.18 kJ kg–1 K–1. [4 marks] Answers: 0.5 K per hour, 4 K

b) If the cost of electricity in that part of Australia is 0.25 $ per kWh, how much has the family saved by using solar power instead of purchasing electricity to heat the pool directly for 8 hours? [2 marks] Answer: $46

c) The additional 1 kW of electricity generated by the solar panels is available to run the centrifugal pump that pumps the water from the swimming pool through the heat pump (a negligible amount of this energy ends up as heat energy in the water; most is lost to the atmosphere). Figure 2.1 shows the characteristic curves for the pump at different speeds. The pump sits below the pool, with pipework totalling 11 m of 25.4 mm internal diameter smooth plastic piping. There is a sharp-edged inlet (KL = 0.5) and exit back into the pool (KL = 1.0), with two 90° bends (KL = 0.85 each) in the pipework on both the suction and discharge sides (four 90° bends altogether).

i) Write down the extended form of Bernoulli’s equation, including terms to account for the head loss due to friction and the head contributed by the pump. [3 marks]

ii) In this system the head loss due to friction must be just balanced by the pressure head increase delivered by the pump. Show that the head loss due to friction can be expressed as a function of the volumetric flowrate of fluid through the pump, Q, as follows: 2 ?h f ? 20 00 00KQ [6 marks]

iii) For a flowrate of 120 litres min–1, use the Moody chart on page 3 to show that the Fanning friction factor is around 0.0044, and show that the head loss due to friction is 10 m. Assume the density of water is 1000 kg m–3 and the viscosity is 0.001 Pa s. [10 marks]

iv) From the characteristic curves shown in Figure 2.1, identify the pump speed in rpm required to deliver the desired flowrate of 120 litres min–1. Explain your reasoning. [2 marks] Answer: 2000 rpm

v) Calculate the power drawn by the pump to deliver 120 litres min–1, if the pump efficiency is 65%. [3 marks] Answer: 300 W

Answer 1

a) The energy balance equation can be written as

Rate of thermal energy gained by swimming pool = thermal energy supplied by heat pump

If the process goes on for 8 hr then according to above equation

b) As per question totak kwh becomes =

So total cost becomes =

c)

1)The extended form of bernouli's equation

2) more information needed as the final form of Q is not understandable