What is the energy requirement, in \(\mathrm{kW}\), for a pump that is 75 percent efficient if it increases the pressure of \(10 \mathrm{~kg} / \mathrm{s}\) of water from \(10 \mathrm{kPa}\) to \(6 \mathrm{MPa}\) ? a) 60 c) 80 b) 70 d) 90

Pump efficiency is a measure of how well a pump converts the input electrical energy into hydraulic energy to move a fluid. In simpler terms, it tells us what portion of the energy provided to the pump is actually used for pumping the fluid, without being wasted as heat or noise. This is crucial in engineering thermodynamics because it affects the overall performance and cost-effectiveness of pumping systems.

In the exercise, the pump's efficiency is given as 75%, which implies that out of the total energy supplied to the pump, only three-quarters are effectively utilized in increasing the water's pressure. The rest may be lost due to friction, leakage, or other inefficiencies within the pump. Therefore, to ascertain the actual energy requirement, one must divide the calculated work done by this efficiency factor. Accurate calculation of pump efficiency is essential in designing systems, estimating operating costs, and selecting the right pump for the job.

Fluid mechanics is the study of fluids (liquids and gases) and the forces on them. It is a cornerstone of engineering thermodynamics and applies to a wide range of topics, from the design of water supply systems to the prediction of weather patterns.

In the context of the exercise, understanding fluid dynamics is essential to calculate the work done by the pump. Assuming water is incompressible, which is a common approximation for liquid water under normal conditions, allows us to use a constant specific volume for water in the work-done formula. The incompressibility assumption is a fundamental principle in fluid mechanics that simplifies calculations for liquids, especially when there are significant pressure changes, as seen in the exercise. Without this assumption, the problem would require a more complex analysis that accounts for the compressibility of water.

Energy conversion in engineering thermodynamics involves changing energy from one form to another. In the case of a pump, electrical energy is converted into mechanical energy that increases the potential energy of the fluid being pumped by elevating its pressure. Understanding energy conversion is vital for the development and optimization of various mechanical systems, ensuring they operate efficiently and effectively.

The exercise demonstrates a direct application of energy conversion principles. First, electrical energy is supplied to the pump, after which the pump converts this energy into mechanical energy, quantifiable as the work done on the water. This energy transition is not perfect, due to inefficiencies, and the pump efficiency rating indicates the effectiveness of this conversion. Calculating the energy requirement demands an understanding of how this conversion process affects the system's overall energy needs, emphasizing the importance of energy conversion knowledge in solving practical engineering problems.