A turbine at the bottom of a dam has a flow of liquid water through it. How does that produce po

A turbine at the bottom of a dam has a flow of liquid water...

Key Concepts

Gravitational Potential Energy

This is the energy stored due to the height of the water above the turbine. It is quantified as mgh (mass × gravitational acceleration × height) and represents the primary energy source in a hydroelectric dam where water at elevation has the potential to do work as it descends. When water falls, its potential energy is converted into other forms, making it crucial in considering energy conversion in such systems.

Kinetic Energy

This term accounts for the energy of motion in the fluid. As water accelerates through the turbine, its velocity increases, and its kinetic energy (given by ½mv²) becomes significant. This energy is directly harnessed by the turbine, which converts the fluid’s kinetic energy into mechanical energy and subsequently into electrical energy.

Pressure Energy

Pressure energy, which is a component in the Bernoulli energy equation, represents the energy due to the fluid pressure. In fluid dynamics, the energy available is a combination of pressure potential energy, gravitational potential energy, and kinetic energy. In the context of a turbine, a change in pressure helps drive the fluid flow, which in turn contributes to the overall energy conversion process.

Transcript

00:01 Problem 6 .11 in this problem our turbine is placed at the bottom of a dam so let us first draw a rough sketch of the dam let us say all right this this is the dam and this is the bottom line and obviously here a turbine is placed so there will be this is the bottom line so this is ground level we can have this line and and there will be passes through this dam for the water flow.

00:37 So let's see from this side the water is coming and this is the exit side of the water.

00:47 Left side is the reservoir side.

00:50 So this is the reservoir side and this is the exit side of the turbine.

01:01 Now we see a left -hand side or the reservoir side as upstream and the other side as downstream okay this is damn all right now if we talk about that who which factor is responsible for the power production in this case then we observe here that if we consider two points let us say first point that is on the free surface so basically this was the free surface this symbol is indicated this symbol indicates that this is exposed to the atmospheric pressure so this is the point one that is at the free surface of this liquid surface on upstream side and after some time when water will flow from this turbine then after some time the height of this free surface will decrease and it will come to the let's say at point two so this point one will come to the point two now if we look at the point one and point two then obviously we can observe here that there will be some height difference between these two surfaces one surface corresponding to point one and one corresponding to point two now this height difference will basically will be responsible for the decrease in potential energy so there will be at point one we can say that there will be higher potential energy but at point two there will be lower potential energy this drop in potential energy is basically responsible for the power extraction through this turbine okay so the in the first part they have asked that which is responsible or what produces the power in the power in this case so basically drop in potential energy drop in potential energy is responsible for power production now in second part they have asked which term of energy equation is important so if you look at the energy equation then energy equation suggests that suggests that h plus v squared by two plus g z must remain constant if there is no heat is transferred or there is no work interaction then we can say that the total energy will remain constant now for that in the case of dams we are not we normally neglect the variation in temperature so enthalpy is the term or it is a part of the energy that is related with the temperature so we can say that the enthalpy will be neglected in this case since there we do not consider the variation in temperature of the fluid in case of dams now if we look at the kinetic energy term this is the kinetic energy term so our kinetic energy is also neglected in this case and reason behind this is since if we go for the mass conservation then mass can be written as row mass flow rate can be written as row a v v is the velocity now if we consider the fluids generally that is our consideration is that the fluids are incompressible.

04:49 So we can this term row is constant.

04:54 Now areas in case of dams are very large.

04:58 Now areas are very large and these two products that is a into v have to remain constant...

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