25.2.2. Energy Extraction by Turbines

Now very basic things we should understand it, whenever a pipe exit, that means flow is going out. The pressure head becomes atmospheric pressure, no doubt about that. And that is the reason, the hydraulic gradient lines coincidence with the pipe outlet. So, when the pressure head becomes zero, that is what we said it, in case of open channel flow, when there is no pressure, is pressure is atmospheric pressure, that the surface becomes hydraulic gradient line.

When water flows out of a pipe, the pressure inside the pipe drops to atmospheric pressure at the outlet. This condition causes the hydraulic gradient line, which represents how the pressure in the fluid changes with height, to align with the outlet of the pipe; because at this point, the pressure is no longer providing any head to push the fluid upwards. This understanding is crucial when analyzing fluid systems, especially when comparing open channel flows where pressure is not involved.

Think about a water fountain: as the water exits the fountain and goes into the air, it no longer has the pressure from being contained in pipes; instead, it relies purely on the gravitational pull to fall back down. Similarly, once the water exits the pipe, it’s like the fountain, where it transitions from a pressurized system to an unpressurized one.

Mechanical energy losses due to the frictional effects, which is converting from thermal energy, the causes the energy gradient line, hydraulic gradient line, to a slope downwards in the directions of the flow, that is what I try to explaining to you. There will be energy losses whenever you have the flow systems.

As fluid flows through pipes, it encounters resistance from the pipe walls (friction). This resistance causes energy losses, meaning that not all the energy input into the system can be converted to kinetic or potential energy of the flowing fluid. In a graphical representation, both the energy gradient line and the hydraulic gradient line slope downwards, indicating that energy is being lost along the flow path, predominantly due to friction.

Imagine sliding down a slide at a playground. If the slide is smooth, you go down quickly, but if it is rough, you slow down because of friction. Just like that, fluids lose energy traveling through pipes, particularly when the pipes are rough or damaged, causing them to lose speed and pressure.

As you know it, the pump is transfer from mechanical energy to fluid by rising pressures. So, fluid gains the energy because of the pumping systems by rising its pressures, that is the. Similar way, the turbine does opposite things, that it takes out or extract the mechanical energy from the fluid by dropping it pressure.

Pumps increase the energy of a fluid by acting on it with mechanical energy to raise its pressure and move it along a system. In contrast, turbines extract energy from a moving fluid, causing a drop in pressure as the fluid does work (like rotating the turbine blades). Understanding this relationship is crucial in energy management systems, especially in hydroelectric power generation.

Consider a water wheel at a mill: when moving water hits the blades of the wheel, it turns the wheel, converting the fluid's energy into mechanical work (like grinding grain). Here, the turbine is extracting energy from the water flow, demonstrating how turbines can generate power from moving water.

This mechanical energy what we get it and if I multiply with a mass rate, I will get the work done part, okay. How much of work done we are getting it or how much power we are getting it, maximum ideal power generated by turbines will be m dash and the energy part.

The concept of power in fluid dynamics can be understood through the product of energy and mass flow rate. When we talk about turbines, the power they can generate theoretically can be calculated by multiplying the mass flow rate of the fluid by the energy extracted per unit mass (often related to the drop in height or pressure). This helps engineers design systems that maximize the efficiency and output of turbines.

Imagine a hydroelectric dam. Water from the reservoir has potential energy, which converts to kinetic energy as it flows down to the turbine. The more water that flows per second (mass rate), the more energy (and therefore power) can be produced, similar to how a bigger river can generate more electricity than a small stream.

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