Fluid Mechanics and Thermodynamics Practice Questions

Question 1: Pipe Flow and Pumping

1. The water level in a large reservoir is 10m above a local datum. A 200mm diameter pipe connected to the reservoir is 150m long and is connected to a higher reservoir whose water level is 60m above the same datum.
a) Produce a neat labelled sketch of the initial situation. [3]
b) The intention is to pump water from the lower to the higher reservoir with a target flowrate of 0.2 m3 .s-1 . A pump is introduced at a position 20m from the lower reservoir where the pipe centreline is 5m above the local datum. Calculate the head required of the pump including the effect of the entrance and exit losses in the pipe as well as pipe friction losses. [5]
c) Calculate the pressure in the pipe at the point just upstream of the pump. Explain why it is important to check this pressure. [5]
d) Following these preliminary calculations a more refined estimate is required by recognising that the friction factor depends on Reynolds number and the pipe roughness ks (or ?) of 0.03mm. Using a suitable iterative method with either Colebrook-White transition formula or
the Moody Diagram and including entrance and exit losses, recalculate the head required of the pump to deliver the same volumetric flow rate of 0.2 m3 .s-1 . [7]

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2. A 20-inch (nominal O.D.) steel pipeline is transporting oil from a North Sea offshore rig along the sea bed. At a point where there is a large subsea obstruction the pipe deviates from its straight line direction by an angle of 15 degrees in a horizontal plane, but maintains its diameter. The flow of oil is 0.4m3 /s and the pressure is 20barg.
a) Assuming a design pressure, for sizing only, of 60bar, estimate the pipe thickness and hence the inside diameter from standard sections, using references [1] and [2] if desired. [4]
b) By applying the linear momentum principle, calculate the force that the pipe must provide on the flowing oil to achieve this change in direction. [10]
c) By making clearly stated assumptions about any unknown quantities estimate the size of a mass of concrete at the pipe bend that will be sufficient to provide the forces required to resist the thrust from the pipe using sliding resistance. Remember that the concrete is under water
and its horizontal resistance to sliding will be related to (but not equal to) its vertical weight.

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Include a factor of safety of 2 in your analysis. [6]
[Although often such pipes are trenched this doesn�t really affect the requirement to resist the lateral forces at the bend because support from the sides of the trench cannot be guaranteed on a mobile sea bed. N.B. the concrete is not necessarily wrapped around the pipe, it is a large mass placed on the sea bed to which the pipe bend is securely fixed. Be careful not to use sources that are dealing with bends in a vertical plane.] 2

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3. The data in table Q3 are from a single centrifugal pump.
a) Copy the data and include in your table the electrical input power required at each flow. [5]
b) Three such pumps are to be connected in parallel to a 1200m long pipeline of 200mm diameter with a friction factor of 0.02, connecting two large reservoirs. The static lift between the two reservoirs is 10m. Including local losses (entrance and exit) and pipe friction, plot suitable graphs and determine the duty point. State the head, discharge (flowrate), efficiency and input power at this point. [10]
c) If one of the pumps is taken out of service for maintenance what is the percentage change in discharge and in the required electrical input power. [5]

Table Q3. Centrifugal pump data for question 3.
Q l/s 0 10 20 30 40 50
H m 25 23.2 20.8 17.0 12.4 7.1
Eff % 0 45 65 71 65 45

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4. A heat pump receives heat from the outside air in winter and supplies heat into a house.
a) The outside air temperature is 3 o
C and the house loses heat to the atmosphere at the rate of 5,000 kJ/h per o C difference between the indoors and outdoors. Can the owner purchase a heat pump with 2.5 kW to maintain the house at 20 o C? [10]
b) Determine the lowest outdoor temperature for which the heat pump can still meet the heating requirement of the house. [10]
5. Design a non-ideal Rankine steam power cycle that can achieve a cycle thermal efficiency of at least 40% under the conditions that the turbine has isentropic efficiency of 85% and the pump has isentropic efficiency of 60%.
a) Sketch the T-s diagram for this cycle; label the states, temperature, pressure, entropy, quality, and the remaining parameters that are used to determine your design solution. [10]
b) Demonstrate the suitability of your design with analysis and calculation [10]

The lowest outdoor temperature at which a heat pump can still meet the heating requirements of a house depends on several factors, such as the size and insulation of the house, the efficiency of the heat pump, and the desired indoor temperature.

In general, most air-source heat pumps are designed to operate efficiently in temperatures down to around 25-30 degrees Fahrenheit (-4 to -1 degrees Celsius), but they can continue to operate at lower temperatures. However, as the outdoor temperature drops, the efficiency of the heat pump decreases, meaning it will have to work harder and longer to maintain the desired indoor temperature.

To determine the lowest outdoor temperature at which a heat pump can still meet the heating requirements of a house, it's best to consult with a professional HVAC technician who can evaluate the specific conditions of your home and recommend a suitable heat pump system. They can also advise you on how to properly maintain and operate your heat pump to ensure optimal performance and efficiency.