Principles of Fluid Mechanics Fluid: Fluid is a substance that deforms or flows continuously under the action of a shear stress (force per unit area). In fluid mechanics the term fluid can refer to any liquid or gas. Incompressible and Compressible Fluid: When the density of a fluid does not change substantially (change in density is less than 3%) under the application of pressure then it is called incompressible fluid e.g. water. When the density of a fluid changes substantially (change in density is more than 3%) under the application of pressure then it is called compressible fluid e.g. air. Pressure Head: It is a term used in fluid mechanics to represent the energy of a static fluid due to the pressure exerted on its container. Mathematically it is represented as h= Here, h is the vertical height of the free surface above any point in a liquid at rest and P is the pressure exerted on the bottom of the container. Specific weight: It is the weight per unit volume of a fluid. Mathematically it is represented as Flow rate or Discharge: It is the quantity of fluid (mass or volume) flowing through any closed or open conduit in unit time. Steady Flow: It is the fluid flow in which all the fluid properties at any one point are constant with respect to time. If F is any fluid property, for steady flow Unsteady Flow: It is the fluid flow in which all the fluid properties at any one point are variable with respect to time. If F is any fluid property, for unsteady flow Uniform flow: It is the fluid flow in which all the fluid properties at any time are constant with respect to space variables. If F is any fluid property, for uniform flow P ρg γ = ρg df dt df dt df ds = 0 0 = 0 Non Uniform flow: It is the fluid flow in which all the fluid properties at any time are variable with respect to space variables. If F is any fluid property, for non uniform flow df ds 0
Bernoulli s Equation Assuming that, the fluid flow is steady and the fluid is modeled as incompressible, Newton s second law can be integrated along a streamline to give Bernoulli s Equation in the form: For steady flow, a streamline can be thought of as the path along which a fluid particle moves when traveling from one location in the flow to another location. Each term in the Bernoulli s equation has the unit of pressure. i.e. (Pa or N/m 2 ). This equation indicates that the total sum of the pressure is constant along a streamline although the value of the components can vary depending on the path of the fluid. But the total sum will always be constant. p = static pressure 1 / 2 ρv 2 = dynamic pressure γz = hydrostatic pressure An alternate equivalent to Bernoulli s Equation can be found by dividing both sides of the equation by the specific weight γ. The equation then becomes- Each of the terms in this equation has the units of length and represents a certain type of head. The elevation term, z, is related to the potential energy of the particle and is called the elevation head. The pressure term, p/γ, is called the pressure head and represents the pressure energy of the fluid. The velocity term, V 2 /2g, is the velocity head and represents kinetic energy of the fluid. The Bernoulli equation states that the sum of the pressure head, the velocity head, and the elevation head is constant along a streamline. Application of Bernoulli s Principle The shape of the airplane wings is made in such a way that the shape induces the air flowing over its top surface to flow faster causing the pressure on the upper side of the wing to be lower than the pressure on the underside of the wing. This difference of pressure causes the airplane to achieve elevation. Other notable application of the Bernoulli s Principle is the reverse swing of the cricket ball.
Fluid Machinery Machines that either energize the fluid (pump, fan, blower and compressor) or extract energy from the fluids (turbines) are called fluid machinery. Turbine A turbine is a rotary machine that extracts energy from a liquid or air flow and converts it into useful work. Turbines are classified into the following types according to their principle of operation Impulse Turbine Reaction Turbine Impulse Turbines Fig.: Working Principle of (a) Impulse Turbine (b) Reaction Turbine Principle of Operation: Impulse turbines work on the principle that the high pressure, high velocity fluid is directed onto the moving blades transferring its kinetic energy to the blades. These turbines change the direction of flow of a high velocity fluid or gas jet. The resulting impulse spins the turbine and leaves the fluid flow with diminished kinetic energy. There is no pressure change of the fluid or gas in the turbine rotor blades (the moving blades). All the pressure drop takes place in the stationary blades (the nozzles). Before reaching the turbine, the fluid's pressure head is changed to velocity head by accelerating the fluid with a nozzle. Impulse turbines do not require a pressure casement around the rotor since the fluid jet is created by the nozzle prior to reaching the blading on the rotor. Newton's second law describes the transfer of energy for impulse turbines. Reaction Turbines Principle of Operation: The principle of a pure reaction turbine is that all the energy contained within the fluid is converted to mechanical energy by reaction of the jet of the fluid as it flows over the blades of the rotor. The rotor is forced to rotate as the fluid exhausts the rotor blades according to Newton s 3 rd law of motion. In practice, it is impossible to achieve pure reaction effect as the incoming fluid to the turbine has velocity when it reaches the moving blades. Therefore the fluid on passing across the moving blades imparts some impulse to the blades. The force developed by impulse compared to the force developed by reaction will depend on the rotor speed/fluid flow velocity ratio.
Fig.: Fluid Flow, Pressure and Velocity distribution in Impulse and Reaction Turbines
Pelton Wheel Fig.: Schematic Diagram of Pelton Wheel and Bucket The Pelton wheel is among the most efficient types of water turbines. It is an impulse turbine, meaning that it uses the principle of Newton's second law to extract energy from a jet of fluid. Fig.: Cross Section of Pelton Wheel Bucket and Velocity Diagram of Working Fluid Principles of Operation: In a pelton wheel, nozzles direct forceful streams of water against a series of spoon-shaped buckets mounted around the edge of a wheel. As water flows into the bucket, the direction of the water velocity changes to follow the contour of the bucket. When the water-jet contacts the bucket, the water exerts pressure on the bucket and the water is decelerated as it does a u-turn and flows out the other side of the bucket at low velocity. In the process, the water's momentum is transferred to the turbine. This impulse does work on the turbine. A very small percentage of the water's original kinetic energy will still remain in the water which allows the bucket to be emptied at the same rate it is filled. Thus allowing the water flow to continue uninterrupted. Often two buckets are mounted side-by-side, thus splitting the water jet in half. This balances the side-load forces on the wheel, and helps to ensure smooth, efficient momentum transfer of the fluid jet to the turbine wheel.
Kaplan Turbine Fig.: Schematic Diagram of Kaplan Turbine The Kaplan turbine is a propeller type water turbine which has adjustable blades. Kaplan turbines are now widely used throughout the world in high-flow, low-head power production. Fig.: Cross Section of Kaplan Turbine Principles of Operation: The Kaplan turbine is an inward flow reaction turbine, which means that the working fluid changes pressure as it moves through the turbine and gives up its energy. The inlet is a scroll shaped tube that wraps around the turbine's wicket gate. Water is directed tangentially through the wicket gate and spirals on to a propeller shaped runner, causing it to spin. The outlet is a specially shaped draft tube that helps decelerate the water and recover kinetic energy.
Pumps A pump is a machine which, when interposed in a conduit, transfers energy from some external source to the liquid flowing through the conduit. Classification Pumps are primarily divided into the following categories Rotodynamic Pump Positive Displacement Pump Rotodynamic Pump Rotodynamic pumps (or dynamic pumps) are a type of pump in which kinetic energy is added to the fluid by increasing the flow velocity by using a revolving wheel or rotor or impeller. This increase in kinetic energy is converted to pressure energy (pressure) by utilizing the Bernoulli s Principle. Typical examples of Rotodynamic pumps include centrifugal pump, turbine pump and submersible pump. Centrifugal Pump A centrifugal pump is a rotodynamic pump that uses a rotating impeller to increase the pressure and flowrate of a fluid. Centrifugal pumps are the most common type of pump used to move liquids through a piping system. The fluid enters the pump impeller along or near to the rotating axis through a hole called impeller eye. Fluid is then accelerated by the impeller rotation. Fluid flows radially outward into a diffuser or volute chamber, from where it exits into the downstream piping system. In the volute chamber the kinetic energy increased by the impeller is converted into pressure energy. Centrifugal pumps are typically used for large discharge through smaller heads. Fig.: Centrifugal Pump Fig.: Cross Section of Centrifugal Pump Fig.: Volute Casing and Impeller
Submersible Pump: A submersible pump is a device which has a hermetically sealed motor close-coupled to the pump body. The whole assembly is submerged in the fluid to be pumped. These types of pumps are used to collect water or crude oil from deep down below the ground level. Turbine Pump A turbine pump is a device which has a motor coupled to the pump body by a long shaft. The pump body is submerged into the fluid to be pumped but the motor stays over the ground. This type of pump is used for collecting high quantity of water from low depths. Fig.: Turbine Pump Fig.: Submersible Pump
Positive Displacement Pump A positive displacement pump causes a fluid to move by trapping a fixed amount of it then forcing (displacing) that trapped volume into the discharge pipe. The rate of fluid flow consequently depends almost wholly on the speed of rotation. Positive Displacement Pumps can be further classified into the following two types Rotary Type: Gear Pump, Lobe Pump Reciprocating Type: Piston Pump, Diaphram Pump Rotary Type Positive displacement rotary pumps are pumps that move fluid using the principles of rotation. The vacuum created by the rotation of the pump captures and draws in the liquid. The fluid is then squeezed out to the delivery side. Fig.: Gear Pump Gear Pump: Gear pumps are the simplest type of rotary pumps, consisting of two gears laid out side-by-side with their teeth enmeshed. The gears turn away from each other, creating a current that traps fluid between the teeth on the gears and the outer casing, eventually releasing the fluid on the discharge side of the pump as the teeth mesh and go around again. Fig.: Lobe Pump Lobe Pump: A lobe pump works in the same principle as the gear pump using shapes called lobes instead of gears.
Reciprocating Type Fig.: Piston Pump A reciprocating pump consists of a cylinder with a reciprocating plunger in it. The suction and discharge valves are mounted in the head of the cylinder. In the suction stroke the plunger retracts and the suction valves open causing suction of fluid into the cylinder. In the forward stroke the plunger pushes the liquid out of the discharge valve. Packed gland is a seal to prevent leakage. Comparison between Rotodynamic Pump and Positive Displacement Pump Rotodynamic Pumps Positive Displacement Pumps Runs at very high speed Cannot run at high speeds Continuous delivery Pulsating delivery (Reciprocating) High Flow Rate Low Flow Rate Low Pressure Developed at Discharge High Pressure Developed at Discharge Suitable for Domestic Water Supply Suitable for Chemical Dosing Started with discharge valve closed Started with discharge valve open Fan, Blower and Compressor Fan, blower and compressor are used for the purpose of energizing the gaseous fluids only. Fan increases the velocity of the fluid but it does not increase the pressure of the fluid by any significant amount. Blower increases the velocity of the fluid and also increases the pressure upto 2 atm. Compressor increases the velocity of the fluid and simultaneously increases the pressure greater than 2 atm. As for example a typical compressor used in 250 MW Gas Turbine power plant can increase the pressure of the air taken from the ambient from 1 atm upto 17 atm.