Solved Problems

Example

Problem: A pump lifts 50 L/s of water against a static head of 30 m. The friction loss in the pipe is 10 m. The pump efficiency is 75%. Calculate the power required.

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Example

Problem: A pump is installed 3 m above the water level (hs=3h_s = 3 m). Atmospheric pressure is 101 kPa. Vapor pressure is 2.34 kPa. Suction friction loss is 1.5 m. Find the available NPSH.

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Example

Problem 3: Pelton Wheel Power A Pelton wheel works under a head of 500 m500 \text{ m} and delivers 10 MW10 \text{ MW}. The overall efficiency is 85%85\%. Find the flow rate required. Assume the coefficient of velocity for the nozzle is Cv=0.98C_v = 0.98.

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Example

Problem 4: Pump Affinity Laws A centrifugal pump running at 1200 rpm1200 \text{ rpm} delivers 0.2 m3/s0.2 \text{ m}^3\text{/s} against a head of 20 m20 \text{ m}. If the speed is increased to 1500 rpm1500 \text{ rpm}, what are the new discharge and head?

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Case Study 1: Pumped-Storage Hydroelectricity

Context: Managing power grid loads requires storing excess energy for peak demand times.
Application: Pumped-storage plants use reversible pump-turbines. During low-demand periods (nighttime), excess electrical energy from the grid is used to pump water from a lower reservoir to an upper reservoir. The machine operates as a centrifugal pump. During peak demand (daytime), the water is released back down to the lower reservoir, and the same machine operates as a reaction turbine (like a Francis turbine) to generate electricity. This dual capability is vital for grid stability, especially with the integration of variable renewable energy sources.

Case Study 2: Selecting Turbines based on Head

Context: Different turbine designs are optimized for specific site conditions.
Application: The choice of hydraulic turbine is dictated by the available head and flow. For very high heads and low flow rates (e.g., steep mountain streams), an impulse turbine like a Pelton wheel is used. For medium heads and flows, a Francis reaction turbine is standard. For very low heads (like run-of-the-river dams or tidal barrages) with massive flow rates, an axial-flow Kaplan turbine is required because its adjustable propeller blades maintain high efficiency even as the low head fluctuates.