The cylinder is connected to the sump by a suction pipe and to the delivery tank by a delivery pipe. Through the suction valve, liquid can only be admitted into the cylinder and through the delivery valve, liquid can only be discharged into the delivery pipe. When the pump is started for the first time or after a long period of time, air is drawn from the suction pipe during the suction stroke, while the delivery valve is closed.
During the delivery stroke, air in the cylinder is forced out by the pressure of the piston into the delivery pipe, while the suction valve is closed. If there is only one suction and one delivery pipe and the liquid is filled from only one side of the piston, it is called a single-acting reciprocating pump. A double acting reciprocating pump has two suction and two delivery pipes, Liquid is received on both sides of the piston in the cylinder and is delivered in the respective delivery pipes.
Piston pump slip is defined as the difference between theoretical and actual flow. Here, Cd is known as flow coefficient and is defined as the ratio of actual flow to theoretical flow. Thus, some water is forced into the delivery pipe before the delivery stroke actually begins.
If the velocity of the water in the supply pipe is 1.4 m/s, the pump efficiency is 90% and the slip is 2%, determine the pump speed and the input power delivered.
Solution
Effect of piston acceleration on velocity and pressure in suction and delivery pipes. Note: If the piston SHM assumption is not valid due to the shorter connecting rod length, then the acceleration head in the pipes is given by: 𝜃(𝐿 . 𝑐/𝑟).
This indicates that the friction head is parabolic
An indicator diagram of a reciprocating pump is a graph that shows the change in pressure in the cylinder with the displacement of the piston at different stages of the piston strokes. The area of the indicator diagram represents the work done by the pump per unit weight of fluid in one full rotation of the crank. Total work done in one complete revolution of the crank per unit weight of fluid (or total head) = 𝐻𝑆 + 𝐻.
The unit weight of liquid pumped in one complete revolution of the crank is 𝜸𝑨𝑳
3 𝐻 𝑓𝑑𝑚 Total work done in one complete revolution of the crank
If the absolute pressure inside the cylinder (i.e. absolute pressure on the piston or piston) is less than or equal to vapor pressure of the liquid, separation (cavitation) will occur. One is at the beginning of the suction stroke and another is at the end of the delivery stroke. The absolute pressure at the cylinder or on the piston at any moment during the suction stroke,.
It can be proved that 𝐻𝑐𝑦𝑙 is minimal when 𝜃 = 0, i.e. at the beginning of the suction movement. Taking the water vapor pressure at standard atmospheric conditions as 2.5 m absolute water, we can see that to prevent separation (cavitation) during suction 𝐻𝑐𝑦𝑙 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 │𝑠𝑢𝑐𝑡𝑖 𝑜𝑛 ≥ 2.5, 𝑖. Thus, by equating the above equation and substituting 𝜔 = 2𝜋𝑁60, we can determine the maximum speed of the pump.
The absolute pressure in the cylinder or in the piston at any moment during the delivery stroke. It can be proved that 𝐻𝑐𝑦𝑙 is minimum when 𝜃 = 180, i.e., at the end of the delivery stroke. Usually one air container is connected to the suction side and one to the delivery pipe.
The compressed air at the top contracts or expands to absorb most pressure fluctuations. The acceleration head remains limited to a shorter length between the pump and the air reservoirs, i.e. between 𝑙𝑠2 and 𝑙𝑑2. The air tanks equalize the flow in the suction and supply pipes, and the flow is continuous beyond the air tanks.
By mounting the air container as close to the pump as possible, the length of the pipe in which the acceleration height occurs is reduced. This reduces the acceleration head and the pump can be run at a much higher speed without risk of separation. As the acceleration head and friction head are reduced significantly, the work done is also reduced and thus the power input is also reduced.
Delivery Pipe
Suction Pipe
Work done and Power required for Pumps fitted with Air Vessels
Work done when air vessel is NOT fitted
Work done when air vessel is fitted
Work saved in percentage for single acting pump
Work saved in percentage For double acting pump
The length of the suction pipe is 10 m and the diameter is 75 mm. i) Find the acceleration head at the beginning, middle and end of the suction stroke. ii). If the suction head is 3 m, determine the pressure head in the cylinder at the beginning of the stroke when the pump is running at 30 rpm. iii) Under this circumstance, what can be the maximum operating speed of the pump without separation (cavitation). If the split occurs at 78.46 kPa under atmospheric pressure when the pump runs at 45 rpm, find the diameter of the suction pipe without the split.
Problem–8: A single acting reciprocating pump has a piston of 200 mm diameter with a crank of radius 400 mm. Problem–9: A double acting single cylinder reciprocating pump has a piston of 300 mm diameter and a stroke of 375 mm. Find the diameter of the suction pipe so that the minimum pressure head determined by cavitation considerations is not violated.
When the pump is running at 60 rpm, find the smallest diameter of the suction pipe for no separation. If the crank speed is 25 rpm, determine the minimum diameter of the suction pipe to prevent the occurrence of cavitation. The static suction head is 4 m, the diameter of the suction pipe is 75 mm and the length of the suction pipe is 8 m.
One air vessel is placed very close to the cylinder on the suction side and another at a distance of 3 m from the cylinder on the delivery side. Problem–14: A single acting reciprocating pump has an air vessel on the delivery side located very close to the cylinder. Problem-1: A single acting reciprocating pump has piston diameter 300 mm, stroke length 500 mm, rotational speed 40 rpm and total (water) lift 25 m.
If the actual discharge at the pump outlet is 1380 litres/minute, calculate the slip, discharge coefficient and theoretical power in kW required to drive the pump. Problem 3: For a single-acting piston pump, the piston diameter is 150 mm, the stroke length is 300 mm, the speed is 50 rpm and the water must be pumped over 18 m. Estimate the maximum velocity and acceleration in the suction pipe with a diameter of 200 mm and the pressure pipe with a diameter of 250 mm.
The water surface from which the pump draws water is 5 m below the axis of the pump cylinder. If the pump runs at 30 rpm, find the pressure in the cylinder at the beginning, middle, and end of the suction stroke.
