Hydraulic Machines - Essay Example

Impact of a jet onto vanes The liquid comes out in the form of a jet from the outlet of a nozzle, which is fitted to a pipe through which the liquid is flowing under pressure. If some plate, fixed or moving, is placed in the path of the jet, a force is exerted by the jet on the plate. This force is called impact of jet, and is obtained from Newton's second law of motion or from impulse-momentum equation. Force exerted on the inclined plate, moving with a uniform velocity in the direction of a the jet V = absolute velocity of jet of water u = velocity of the plate in the direction of jet a = cross-sectional area of jet = angle between the jet and the plate Relative velocity of the jet = V-u Mass of water striking per second = a(V-u) If the plate is smooth and loss of energy due to impact of the jet is assumed to be zero, the jet of water will leave the inclined vane with a velocity equal to (V-u). Force exerted by the jet in the direction normal to the plate is given as Fn = Mass striking pr second (initial velocity in the normal direction with which jet strikes - final velocity) = a(V-u)[ (V-u)sin - 0)] = a(V-u)2sin This normal force can be divided into two components namely Fx and Fy in the direction of jet and in a direction perpendicular to the jet respectively. Fx = Fn sin = a(V-u)2sin2 Fy = Fn cos = a(V-u)2sin cos Work done per second by the jet on the plate = Fx (Distance per second in x-direction) = Fx u = a(V-u)2sin2 u = a(V-u)2.u.sin2 kgf-m/sec or N m/s. Force exerted on the hemispherical plate, moving with a uniform velocity in the direction of a the jet After impact, the jet leaves the vane with its direction opposite to the direction of impact, since the vane is hemispherical in shape. Relative velocity with which the jet strikes the curved vane = V-u Relative velocity with which the jet leaves the curved vane (assuming that the plate is smooth and the loss of energy due to impact is zero) = V-u Mass of water striking per second = a(V-u) Therefore, force exerted by the jet in the direction of the jet is given as Fx= Mass striking pr second (initial velocity in the normal direction with which jet strikes - final velocity) = a (V - u)[ (V - u) - (- (V - u))] = 2a(V-u)2 Efficiency of the vane = Work done per second Kinetic energy per second Operating principles of common turbomachines Introduction Turbomachines or turbines are defined as the hydraulic machines which convert hydraulic machines into mechanical energy. This mechanical energy is used in running an electric generator which is directly coupled to the shaft of the turbine. If the water flows parallel to the axis of the rotation of the shaft, the turbine is known as axial flow turbine. If the head at the inlet of the turbine is the sum of pressure energy and kinetic energy and during the flow of water through runner a part of pressure energy is converted into kinetic energy, the turbine is known as reaction turbine. Efficiencies of a turbine a) Hydraulic efficiency: It is defined as the ratio of power developed by the runner of a turbine (runner is a rotating part of a turbine and on the runner vanes are fixed) to the power supplied by the water at the inlet of the turbine. Power at the inlet is more and this power goes on decreasing as the water flows over the vanes of the turbine due to hydraulic losses as the vanes are not smooth. b) Mechanical efficiency: the power developed by the runner of a turbine is transmitted at the shaft of the turbine. Due to mechanical losses, the power available at the shaft is less than the power developed by the runner. The ratio of power available at the shaft to the power developed by the runner is known as mechanical efficiency of the turbine. c) Volumetric efficiency: the volume of the water striking the runner of a turbine is slightly less than the volume of the water supplied to the turbine. Some water is discharged to the tail race without striking the runner. Thus, the ratio of the volume of water actually striking the runner to the volume of water supplied to the turbine is defined as the volumetric efficiency. d) Overall efficiency: It is defined as the ratio of power available at the shaft of the turbine to the power supplied by the water at the inlet of the turbine. It is the product of hydraulic efficiency and mechanical efficiency. Pelton Wheel The Pelton wheel or Pelton turbine is a tangential flow impulse turbine. The water strikes the bucket along the tangent of the runner. The energy available at the inlet of the turbine is only kinetic energy. The pressure at the inlet and outlet of the turbine is atmosphere. This turbine is used for high heads and is named after L. A. Pelton, an American Engineer. Francis Turbine The inward flow reaction turbine having radial discharge at outlet is known as Francis Turbine, after the name of J. B. Francis, an American engineer who in the beginning designed inward radial flow reaction type of turbine. In the modern Francis Turbine, water enters the runner of the turbine in the radial direction at outlet and leaves in the axial direction at the inlet of the runner. Thus the modern Francis Turbine is a mixed flow type turbine. Kaplan Turbine For the axial flow reaction turbine, the shaft of the turbine is vertical. The lower end of the shaft is made larger which is known as 'hub' or 'boss'. The vanes are fixed on the hub and hence hub acts as a runner for axial flow reaction turbine. If the vanes on the hub are adjustable, the turbine is known as Kaplan Turbine, after the name of V. Kaplan, an Australian engineer. If not, the turbine is known as Propeller Turbine. This turbine is suitable where a large quantity of water at low heads is available. Some important points for Kaplan Turbine are as follows: 1. The peripheral velocity at inlet and outlet are equal. 2. Velocity of flow at inlet and outlet are equal. 3. Area of flow at inlet and outlet are equal. Operating principles of pumps Hydraulic machines which convert mechanical energy into hydraulic energy are called pumps. Hydraulic energy is present in the form of pressure energy. Centrifugal Pumps If the mechanical energy is converted into pressure energy by means of centrifugal force acting on the fluid, the hydraulic machine is called centrifugal pump. The centrifugal pump acts as a reverse of an inward radial flow reaction turbine. That is, the flow in centrifugal pumps is in the radial outward directions. The centrifugal pump works on the principle of forced vortex flow which means that when a certain mass of liquid is rotated by an external torque, the rise in pressure head at any point of the rotating liquid takes place. The rise in pressure head at any point of the rotating liquid is proportional to the square of tangential velocity of the liquid at that point. Thus at the outlet of the impeller where radius is more, the rise in pressure head will be more and the liquid will be discharged at the outlet with a high pressure head. Due to the high pressure head, the liquid can be lifted to a high level. Efficiencies: a) Manometric efficiency: The ratio of manometric head to the head imparted by the impeller to the water is known as manometric efficiency. b) Mechanical efficiency: The ratio of the power available at the impeller to the power at the shaft is known as the mechanical efficiency. c) Overall efficiency: it is defined as the ratio of the power output of the pump to the power input to the pump. It is the product of manometric efficiency and mechanical efficiency. Reciprocating Pumps If the mechanical energy is converted into pressure energy by sucking the liquid into a cylinder in which a piston is reciprocating (moving backwards and forwards), which exerts the thrust on the liquid and increases its hydraulic energy, the pump is called reciprocating pump. In a single acting reciprocating pump, a piston moves backwards and forwards in a close fitting cylinder. The movement of the piston is obtained by connecting the piston rod o crank by means of a connecting rod. The crank is rotated by means of an electric motor. Suction and delivery pipes with suction valve and delivery valve are connected to the cylinder. These valves allow water to flow in one direction only (one way valves). Suction valve allows water from suction pipe to the cylinder while delivery valve allows water from cylinder to delivery pipe only. Read More