--- title: "Reciprocating pump working, slip and air vessel" subject: "Fluid Machines" chapter: 4 key: "semester_5/fluid_machines:reciprocating-pump-slip-air-vessel" source: https://www.bctengineer.com/q/semester_5/fluid_machines/reciprocating-pump-slip-air-vessel site: BCT Engineering --- # Reciprocating pump working, slip and air vessel Fluid Machines · Chapter 4: Pump - Asked in: year not given, 5+4 marks - Video: [39) Air Vessels & Slip : Reciprocating Pump | Working - Hindi | F.M ~ Basics](https://www.youtube.com/watch?v=HHtygDpROC0) — Defence and SSC Exam - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/fluid_machines/reciprocating-pump-slip-air-vessel - Whole chapter: https://www.bctengineer.com/md/semester_5/fluid_machines/chapter-4 ## Question Explain the working of a single-acting reciprocating pump with its ideal indicator diagram and the function of air vessels. A single-acting reciprocating pump has a plunger of 150 mm diameter and stroke 300 mm, running at 60 rpm. It delivers 5.0 L/s of water against a suction head of 3.5 m and a delivery head of 22 m. Find the theoretical discharge, slip and coefficient of discharge, and the power required if the overall efficiency is 80 %. ## Short answer A single-acting pump draws water on the suction stroke and delivers on the delivery stroke; its ideal indicator diagram is a rectangle. Air vessels maintain nearly uniform pipe flow and reduce pressure surges. Theoretical discharge ALN/60 = 5.30 L/s, slip = 0.30 L/s (5.7%), coefficient of discharge = 0.943, required shaft power = 1.56 kW. ## Answer #### Working of a single-acting pump ```text Delivery valve (opens on delivery stroke) ___|___ | ___ | Cylinder ======|=|___|=|=====> piston / plunger (crank + connecting rod) |_______| Suction valve (opens on suction stroke) | Suction pipe -> sump ``` - **Suction stroke:** the piston moves away from the cylinder cover, creating a vacuum. The delivery valve is held closed, the suction valve opens, and water is pushed into the cylinder by atmospheric pressure. - **Delivery stroke:** the piston moves forward and compresses the water; the suction valve closes, the delivery valve opens, and water is forced into the delivery pipe. - One revolution of the crank gives one suction and one delivery stroke, so discharge is intermittent (only for half the revolution). **Ideal indicator diagram:** a plot of pressure head in the cylinder against piston displacement (stroke) is a rectangle: a horizontal line at $H_s$ below the atmosphere for suction, and a horizontal line at $H_d$ above the atmosphere for delivery. The height of the diagram is $(H_s+H_d)$ and its area represents work per stroke. ```text H Hd |-----------------------| delivery | | Hatm --------------------------- | | Hs |-----------------------| suction 0 L (stroke) ``` **Air vessels:** closed chambers with air at the top, fixed on the suction and delivery pipes close to the cylinder. The air is compressed when the flow is more than the mean and expands when the flow is less than the mean. Thus they: 1. Make the flow in the pipes nearly **uniform**, avoiding acceleration and friction head loss in the long pipes; 2. Reduce the **pressure fluctuation** and shock, so the pump can run at higher speed and with less risk of separation; 3. Save about 80 to 85 % of the work lost in friction in a delivery pipe for a single-acting pump (power saved). #### Numerical **Given:** $D=0.15$ m, $L=0.3$ m, $N=60$ rpm, $Q_{act}=5.0$ L/s, $H_s=3.5$ m, $H_d=22$ m, $\eta_o=0.80$. Plunger area: $A=\frac{\pi}{4}(0.15)^2=0.01767$ m². Theoretical discharge (single acting): $$ Q_{th}=\frac{ALN}{60}=\frac{0.01767\times0.3\times60}{60}=0.00530\ \text{m}^3/\text{s}=5.30\ \text{L/s} $$ Slip: $$ \text{Slip}=Q_{th}-Q_{act}=0.30\ \text{L/s}\ \ \Big(\text{percentage slip}=\frac{0.30}{5.30}\times100=5.7\%\Big) $$ Coefficient of discharge: $$ C_d=\frac{Q_{act}}{Q_{th}}=\frac{5.0}{5.30}=0.943 $$ Power: total head $H=H_s+H_d=25.5$ m. $$ \begin{aligned} P_{water}&=\rho gQ_{act}(H_s+H_d)=1000\times9.81\times0.005\times25.5=1250.8\ \text{W}\\ P_{shaft}&=\frac{P_{water}}{\eta_o}=\frac{1250.8}{0.80}=1563\ \text{W}=1.56\ \text{kW} \end{aligned} $$ **Answer:** $Q_{th}=5.30$ L/s; slip $=0.30$ L/s ($5.7\%$); $C_d=0.943$; power $=1.56$ kW. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In a single-acting reciprocating pump, what happens in one crank revolution? A. Two suction and two delivery strokes B. One suction and one delivery stroke, so delivery is intermittent C. Continuous delivery with no suction D. Only a delivery stroke Answer: B. Water is delivered only during half of each revolution, so the discharge is intermittent. (Key point: Strokes of single-acting pump) 2. What is the main function of an air vessel? A. To increase the discharge by adding air B. To make flow in the pipes nearly uniform and reduce pressure fluctuation and friction head C. To prime the pump D. To raise the delivery head Answer: B. The air compresses and expands to absorb flow variation, saving work lost in friction and allowing higher speed. (Key point: Function of air vessels) 3. With Qth = 5.30 L/s and Qact = 5.0 L/s, which is correct? A. Slip = 0.30 L/s and Cd = 0.943 B. Slip = 0.30 L/s and Cd = 1.06 C. Slip = 5.0 L/s and Cd = 0.943 D. Slip = 10.3 L/s and Cd = 0.943 Answer: A. Slip = Qth - Qact and Cd = Qact/Qth = 5.0/5.30. (Key point: Slip and Cd) 4. Which total head is used in the power calculation? A. Hd only B. Hs + Hd = 25.5 m C. Hd - Hs D. Hs only Answer: B. The pump lifts water through suction plus delivery head; P = rho g Q (Hs + Hd) / eta_o = 1.56 kW. 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