Chemical Engineering. Solutions to the Problems in Chemical Engineering

Richardson J.F., Backhurst J.R., Harker J.H.

Chapter 8 Pumping of Fluids - all with Video Answers

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Chapter Questions

Problem 1

A three-stage compressor is required to compress air from $140 \mathrm{kN} / \mathrm{m}^2$ and 283 K to $4000 \mathrm{kN} / \mathrm{m}^2$. Calculate the ideal intermediate pressures, the work required per kilogram of gas, and the isothermal efficiency of the process. It may be assumed that the compression is adiabatic and interstage cooling is provided to cool the air to the initial temperature. Show qualitatively, by means of temperature-entropy diagrams, the effect of unequal work distribution and imperfect intercooling, on the performance of the compressor.

Hast Aggarwal

Numerade Educator

00:00

Problem 2

A twin-cylinder, single-acting compressor, working at 5 Hz , delivers air at $515 \mathrm{kN} / \mathrm{m}^2$ at the rate of $0.2 \mathrm{~m}^3 / \mathrm{s}$. If the diameter of the cylinder is 20 cm , the cylinder clearance ratio $5 \%$, and the temperature of the inlet air 283 K , calculate the length of stroke of the piston and the delivery temperature.

Rashmi Sinha

Numerade Educator

04:12

Problem 3

A single-stage double-acting compressor running at 3 Hz is used to compress air from $110 \mathrm{kN} / \mathrm{m}^2$ and 282 K to $1150 \mathrm{kN} / \mathrm{m}^2$. If the internal diameter of the cylinder is 20 cm , the length of stroke 25 cm , and the piston clearance $5 \%$, calculate:
(a) the maximum capacity of the machine, referred to air at the initial temperature and pressure, and
(b) the theoretical power requirements under isentropic conditions.

Hariprasad Annamalai

Numerade Educator

04:40

Problem 4

Methane is to be compressed from atmospheric pressure to $30 \mathrm{MN} / \mathrm{m}^2$ in four stages. Calculate the ideal intermediate pressures and the work required per kilogram of gas. Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on a temperature-entropy diagram the effect of imperfect intercooling on the work done at each stage.

Naman Kumar

Numerade Educator

02:49

Problem 5

An air-lift raises $0.01 \mathrm{~m}^3 / \mathrm{s}$ of water from a well 100 m deep through a 100 mm diameter pipe. The level of the water is 40 m below the surface. The air consumed is $0.1 \mathrm{~m}^3 / \mathrm{s}$ of free air compressed to $800 \mathrm{kN} / \mathrm{m}^2$. Calculate the efficiency of the pump and the mean velocity of the mixture in the pipe.

Mayukh Banik

Numerade Educator

10:05

Problem 6

In a single-stage compressor: Suction pressure $=101.3 \mathrm{kN} / \mathrm{m}^2$. Suction temperature $=$ 283 K . Final pressure $=380 \mathrm{kN} / \mathrm{m}^2$. If each new charge is heated 18 deg K by contact with the clearance gases, calculate the maximum temperature attained in the cylinder.

Khoobchandra Agrawal

Numerade Educator

Problem 7

A single-acting reciprocating pump has a cylinder diameter of 115 mm and a stroke of 230 mm . The suction line is 6 m long and 50 mm diameter and the level of the water in the suction tank is 3 m below the cylinder of the pump. What is the maximum speed at which the pump can run without an air vessel if separation is not to occur in the suction line? The piston undergoes approximately simple harmonic motion. Atmospheric pressure is equivalent to a head of 10.4 m of water and separation occurs at pressure corresponding to a head of 1.22 m of water.

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02:11

Problem 8

An air-lift pump is used for raising $0.8 \mathrm{1} / \mathrm{s}$ of a liquid of density $1200 \mathrm{~kg} / \mathrm{m}^3$ to a height of 20 m . Air is available at $450 \mathrm{kN} / \mathrm{m}^2$. If the efficiency of the pump is $30 \%$, calculate the power requirement, assuming isentropic compression of the air $(\gamma=1.4)$.

Eric Mockensturm

Numerade Educator

00:00

Problem 9

A single-acting air compressor supplies $0.1 \mathrm{~m}^3 / \mathrm{s}$ of air (at STP) compressed to $380 \mathrm{kN} / \mathrm{m}^2$ from $101.3 \mathrm{kN} / \mathrm{m}^2$ pressure. If the suction temperature is 288.5 K , the stroke is 250 mm , and the speed is 4 Hz , find the cylinder diameter. Assume the cylinder clearance is $4 \%$ and compression and re-expansion are isentropic $(\gamma=1.4)$. What is the theoretical power required for the compression?

Rashmi Sinha

Numerade Educator

01:07

Problem 10

Air at 290 K is compressed from 101.3 to $2000 \mathrm{kN} / \mathrm{m}^2$ pressure in a two-stage compressor operating with a mechanical efficiency of $85 \%$. The relation between pressure and volume during the compression stroke and expansion of the clearance gas is $P V^{1.25}=$ constant. The compression ratio in each of the two cylinders is the same and the interstage cooler may be taken as perfectly efficient. If the clearances in the two cylinders are $4 \%$ and $5 \%$ respectively, calculate:
(a) the work of compression per unit mass of gas compressed;
(b) the isothermal efficiency;
(c) the isentropic efficiency $(\gamma=1.4)$;
(d) the ratio of the swept volumes in the two cylinders.

Manik Pulyani

Numerade Educator

02:56

Problem 11

Explain briefly the significance of the "specific speed" of a centrifugal or axial-flow pump. A pump is designed to be driven at 10 Hz and to operate at a maximum efficiency when delivering $0.4 \mathrm{~m}^3 / \mathrm{s}$ of water against a head of 20 m . Calculate the specific speed. What type of pump does this value suggest? A pump built for these operating conditions has a measured overall efficiency of $70 \%$. The same pump is now required to deliver water at 30 m head. At what speed should the pump be driven if it is to operate at maximum efficiency? What will be the new rate of delivery and the power required?

Chai Santi

Numerade Educator

01:39

Problem 12

A centrifugal pump is to be used to extract water from a condenser in which the vacuum is 640 mm of mercury. At the rated discharge, the net positive suction head must be at least 3 m above the cavitation vapour pressure of 710 mm mercury vacuum. If losses in the suction pipe account for a head of 1.5 m , what must be the least height of the liquid level in the condenser above the pump inlet?

Narayan Hari

Numerade Educator

01:38

Problem 13

What is meant by the Net Positive Suction Head (NPSH) required by a pump? Explain why it exists and how it can be made as low as possible. What happens if the necessary NPSH is not provided?

A centrifugal pump is to be used to circulate liquid of density $800 \mathrm{~kg} / \mathrm{m}^3$ and viscosity $0.5 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$ from the reboiler of a distillation column through a vaporiser at the rate of $400 \mathrm{~cm}^3 / \mathrm{s}$, and to introduce the superheated liquid above the vapour space in the reboiler which contains liquid to a depth of 0.7 m . Suggest a suitable layout if a smooth-bore 25 mm pipe is to be used. The pressure of the vapour in the reboiler is $1 \mathrm{kN} / \mathrm{m}^2$ and the NPSH required by the pump is 2 m of liquid.
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Chai Santi

Numerade Educator

06:38

Problem 14

$1250 \mathrm{~cm}^3 / \mathrm{s}$ of water is to be pumped through a steel pipe, 25 mm diameter and 30 m long, to a tank 12 m higher than its reservoir. Calculate the approximate power required. What type of pump would you install for the purpose and what power motor (in kW ) would you provide? Viscosity of water $=1.30 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$. Density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$.

Rashmi Sinha

Numerade Educator

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Problem 15

Calculate the pressure drop in, and the power required to operate, a condenser consisting of 400 tubes, 4.5 m long and 10 mm internal diameter. The coefficient of contraction at the entrance of the tubes is 0.6 , and $0.04 \mathrm{~m}^3 / \mathrm{s}$ of water is to be pumped through the condenser.

Susan Hallstrom

Numerade Educator

12:49

Problem 16

$75 \%$ sulphuric acid, of density $1650 \mathrm{~kg} / \mathrm{m}^3$ and viscosity $8.6 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$, is to be pumped for 0.8 km along a 50 mm internal diameter pipe at the rate of $3.0 \mathrm{~kg} / \mathrm{s}$, and then raised vertically 15 m by the pump. If the pump is electrically driven and has an efficiency of $50 \%$, what power will be required? What type of pump would you use and of what material would you construct the pump and pipe?

Ronald Prasad

Numerade Educator

12:49

Problem 17

$60 \%$ sulphuric acid is to be pumped at the rate of $4000 \mathrm{~cm}^3 / \mathrm{s}$ through a lead pipe 25 mm diameter and raised to a height of 25 m . The pipe is 30 m long and includes two right-angled bends. Calculate the theoretical power required. The density of the acid is $1531 \mathrm{~kg} / \mathrm{m}^3$ and its kinematic viscosity is $4.25 \times 10^{-5} \mathrm{~m}^2 / \mathrm{s}$. The density of water may be taken as $1000 \mathrm{~kg} / \mathrm{m}^3$.

Ronald Prasad

Numerade Educator

12:49

Problem 18

$1.3 \mathrm{~kg} / \mathrm{s}$ of $98 \%$ sulphuric acid is to be pumped through a 25 mm diameter pipe, 30 m long, to a tank 12 m higher than its reservoir. Calculate the power required and indicate the type of pump and material of construction of the line that you would choose. Viscosity of acid $=0.025 \mathrm{~N} \mathrm{~s} / \mathrm{m}^2$. Density $=1840 \mathrm{~kg} / \mathrm{m}^3$.

Ronald Prasad

Numerade Educator

05:04

Problem 19

A petroleum fraction is pumped 2 km from a distillation plant to storage tanks through a mild steel pipeline, 150 mm in diameter, at the rate of $0.04 \mathrm{~m}^3 / \mathrm{s}$. What is the pressure drop along the pipe and the power supplied to the pumping unit if it has an efficiency of $50 \%$ ? The pump impeller is eroded and the pressure at its delivery falls to one half. By how much is the flowrate reduced? Density of the liquid $=705 \mathrm{~kg} / \mathrm{m}^3$. Viscosity of the liquid $=0.5 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$. Roughness of pipe surface $=0.004 \mathrm{~mm}$.

Nicholas Mogoi

Numerade Educator

01:28

Problem 20

Calculate the power required to pump oil of density $850 \mathrm{~kg} / \mathrm{m}^3$ and viscosity $3 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$ at $4000 \mathrm{~cm}^3 / \mathrm{s}$ through a 50 mm pipeline 100 m long, the outlet of which is 15 m higher than the inlet. The efficiency of the pump is $50 \%$. What effect does the nature of the surface of the pipe have on the resistance?

Penny Riley

Numerade Educator

06:38

Problem 21

600 litres $/ \mathrm{s}$ of water at 320 K is pumped in a 40 mm i.d. pipe through a length of 150 m in a horizontal direction and up through a vertical height of 10 m . In the pipe there is a control valve which may be taken as equivalent to 200 pipe diameters and other pipe fittings equivalent to 60 pipe diameters. Also in the line there is a heat exchanger across which there is a loss in head of 1.5 m of water. If the main pipe has a roughness of 0.0002 m , what power must be delivered to the pump if the unit is $60 \%$ efficient?

Rashmi Sinha

Numerade Educator

01:28

Problem 22

A pump developing a pressure of $800 \mathrm{kN} / \mathrm{m}^2$ is used to pump water through a 150 mm pipe 300 m long to a reservoir 60 m higher. With the valves fully open, the flowrate obtained is $0.05 \mathrm{~m}^3 / \mathrm{s}$. As a result of corrosion and scaling the effective absolute roughness of the pipe surface increases by a factor of 10 . By what percentage is the flowrate reduced? Viscosity of water $=1 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$.

Kratika Bhadauria

Numerade Educator