25.5.1. Mass Conservation

And okay, we are not discussing about open channel flow heads, but in case of open channel flow, the hydraulic gradient lines coincides with the free surface of the liquid okay. Because there is no pressure head. So, whatever the water surface free surface, that what will be hydraulic gradient line and the energy gradient lines will have a included the velocity head above the free surface.

In open channel flow, the hydraulic gradient line aligns with the free surface of the liquid. This is because, unlike in closed systems, there is no pressure head acting in open channels. The hydraulic gradient hinges on the water's free surface, indicating how energy flows through this system. The energy gradient line, on the other hand, not only includes the hydraulic gradient but also adds the velocity head, which contributes to total energy measured in the system.

Imagine a river where the water naturally flows and the surface of the water is what you can see. The very top of the water represents the hydraulic gradient line since there’s no enclosed pressure pushing the water down like you would find in pipes. The energy gradient might be likened to a surfer riding a wave, who has not just the height of the wave (hydraulic gradient) but also the speed with which they are moving down the wave (velocity head).

But in case of the pipes, we can have a piezometer to measure it, what could be the hydraulic gradient lines.

In pipe systems, we utilize tools like piezometers to directly measure the hydraulic gradient. A piezometer is a device that gauges fluid pressure. When fluid flows through a pipe, knowing the pressure at various points allows us to determine how the hydraulic gradient changes. This is essential for understanding the flow dynamics and energy losses within the pipe system.

Think of measuring water levels in different buckets lined up in a row—in this scenario, the piezometer acts as your measuring stick. Just like you can see how high the water level is in each bucket (reflecting the pressure at those points), the piezometer helps us visually track how the hydraulic gradient varies within the pipe system.

Mechanical energy losses due to the frictional effects cause the energy gradient line, hydraulic gradient line, to slope downwards in the direction of the flow.

As fluid flows through pipes, mechanical energy is lost mainly due to friction. This loss results in a downward slope of both the energy gradient line and the hydraulic gradient line. Essentially, as fluid progresses through the system, it loses energy, which is reflected in these gradients declining as they are measured downstream.

Consider sliding down a waterslide; initially, you have high energy at the top, but as you slide down, friction with the slide reduces your speed and energy. Similarly, water flowing through pipes begins with a certain energy level, but friction reduces that energy as the water moves downstream.

The gauge pressure of the fluid is zero at the locations when the hydraulic gradient line intersects the fluids. Pressure in a flow section that lies above the hydraulic gradient line is negative and pressure in a section that lies below the hydraulic gradient line will be the positive value.

Gauge pressure represents the pressure of fluid in relation to atmospheric pressure. When the hydraulic gradient intersects with the fluid, that point is considered to have zero gauge pressure. If the pressure in a flow section is above this line, it is regarded as negative as it falls below atmospheric pressure. Likewise, any pressure below the line is a positive value signifying a higher pressure than that intersection point.

Imagine a balloon floating at a certain height; at that height, the pressure inside is equivalent to the surrounding atmosphere. If you push the balloon down into water, its pressure would increase—this is like being below the hydraulic gradient line (positive pressure). However, if you consider it at the surface of a lake, and the balloon is squeezing lightly, that may feel like it's experiencing a 'negative pressure' relative to the water above it.

As you know it, the pump transfers mechanical energy to fluid by rising pressures. Similar way, the turbine does the opposite things, that it takes out or extract the mechanical energy from the fluid by dropping its pressure.

Pumps and turbines are integral components in fluid systems. Pumps increase the mechanical energy of a fluid, effectively raising its pressure. Conversely, turbines extract this mechanical energy from the fluid, which results in a drop in pressure. In practical applications, you’ll often see pumps in water supply systems, while turbines are common in hydroelectric power generation.

Think of a small bicycle pump—when you pump air, you’re forcing it into the tire, increasing the tire's pressure (as in a pump). Conversely, consider a spinning water wheel in a river; as the water moves over it, the wheel spins and generates energy but also causes the water’s pressure behind it to drop, mimicking the action of a turbine.

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