Fluid Mechanics: Fundamentals and Applications
Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
bartleby

Videos

Textbook Question
Book Icon
Chapter 8, Problem 137P

Water at 15 ° C is to be dischaged froiti a reservoir at a rate of 18 L1s using two horizontal cast iron pipes coiuiected w series and a pump between them The first pipe is 20 w bug and lias a 6-cni diameter, while the second pipe is 35 in long and has a 3-cnt diameter. The water level in the reservoir is 30 w above the centerline of the pipe. The pipe citirance is sharp-edged. and losses associated vitli the cOiUieCtiOfl of the PiliulI) are negligible. Neglecting tite etrect of the kinetic energy correction factor. deterniùie the required plunping head and the minimum pluuping pover to maintain the indicated flow rate.

Expert Solution & Answer
Check Mark
To determine

The required pumping head.

The pumping power required to maintain the flow.

Answer to Problem 137P

The required pumping head is 1296.29m.

The pumping power required to maintain the flow is 228.69kW.

Explanation of Solution

Given information:

The temperature of the water is 15°C, the length of the first pipe is 20m, the diameter of the first pipe is 6cm, length of the second pipe is 35m, the diameter of the second pipe is 3cm and the height of the water level in the reservoir is 30m.

Write the expression for the cross-sectional flow area of the pipe 1.

  A1=π4D12   ....... (I)

Here, the diameter of the pipe one is D1.

Write the expression for the velocity of the liquid.

  V1=QA1   ....... (II)

Here, the discharge through the pipe is Q.

Write the expression for the Reynolds number.

  Re=ρV1D1μ   ....... (III)

Here, the dynamic viscosity of water is μ.

Write the expression for the relative roughness value.

  Rv=εD   ...... (IV)

Here, the equivalent roughness of the pipe is ε.

Write the expression for the head of pipe 1.

  h1=V122g(KL+fL1D1)   ....... (V)

Here, the friction factor is f, the diameter of the pipe one D1 and the length of the pipe 1 L1.

Write the expression for the cross-sectional flow area of the pipe second.

  A2=π4D22   ....... (VI)

Here, the diameter of the pipe second is D2.

Write the expression for the velocity of the liquid for pipe second.

  V2=QA2   ....... (VII)

Write the expression for the Reynolds number.

  Re=ρV2D2μ   ....... (VIII)

Write the expression for the relative roughness value.

  Rv=εD   ....... (IX)

Here, the equivalent roughness of the pipe is ε.

Write the expression for the head of pipe 2.

  h2=V222g(fL2D2)   ....... (X)

Here, the length of the pipe 1 L2.

Write the expression for the total head loss.

  hL=h1+h2   ...... (XI)

Write the expression for the pump head.

  hp=V222g+h1z1  ......(XII)

Here, the gravitational acceleration is g.

Write the expression for the pumping power.

  P=Qρghp  ......(XIII)

Calculation:

Refer to table A-7 "properties of liquid" to obtain the loss coefficient for the pipe as 0.5, density of water as 999.1kg/m3, dynamic coefficient of viscosity of water as 1.138×103kg/ms and roughness of the copper as 0.00026m at the temperature T=15°C.

Substitute 6cm for D1 in Equation (I).

  A1=π4(6cm)2=0.7853(36cm2( 1 m 2 10 4 cm 2 ))=2.8270×103m2

Substitute 2.8270×103m2 for A1 and 18L/s for Q in Equation (II).

  V1=18L/s(2.8270× 10 3m2)=18L/s(2.8270× 10 3m2)( 10 3m31L)=6.366m/s

Substitute 999.1kg/m3 for ρ, 6.366m/s for V, 6cm for D1 and 1.138×103kg/ms for μ in Equation (III).

  Re=(999.1kg/ m 3)(6.366m/s)(6cm)(1.138× 10 3kg/ms)=(999.1kg/ m 3)(6.366m/s)(6cm( 1m 102cm ))(1.138× 10 3kg/ms)=381.611.138×103=335339

Substitute 0.00026m for ε and 6cm for D1 in Equation (IV).

  Rv=0.00026m6cm=0.00026m6cm( 1m 100cm)=0.0043

Refer to chart "the moody's chart" to obtain the friction factor at Reynolds number Re=335339 and relative roughness value Rv=0.0043 as 0.02941.

Substitute 6.366m/s for V1, 9.81m/s2 for g, 0.5 for KL, 0.02941 for f, 20m for L1 and 6cm for D1 in Equation (V).

Substitute 3cm for D2 in Equation (VI).

  A2=π4(3cm)2=0.7853(9cm2( 1 m 2 10 4 cm 2 ))=7.067×104m2

Substitute 7.067×104m2 for A2 and 18L/s for Q in Equation (VII).

  V2=18L/s(7.067× 10 4m2)=18L/s(7.067× 10 4m2)( 10 3m31L)=25.46m/s

Substitute 999.1kg/m3 for ρ, 25.46m/s for V2, 3cm for D2 and 1.138×103kg/ms for μ in Equation (VIII).

Substitute 0.00026m for ε and 3cm for D2 in Equation (IX).

  Rv=0.00026m3cm=0.00026m3cm( 1m 100cm)=0.0086

Refer to chart "the moody's chart" to obtain the friction factor at Reynolds number Re=670783 and relative roughness value Rv=0.0086 as 0.03300.

Substitute 25.46m/s for V2, 9.81m/s2 for g, 0.03300 for f, 35m for L1 and 3cm for D2 in Equation (X).

  h2=( 25.46m/s )22(9.81m/ s 2)(0.03300( 35m)( 3cm))=33.038m((0.03300)( 35m)( 3cm)( 1m 100cm ))=33.038m(38.5)1271.9m

Substitute 1271.9m for h2 and 21.3m for h1 in Equation (XI).

  hL=1271.9m+21.3m=1293.26m

Substitute 1293.26m for hL, 25.46m/s for V2, 9.81m/s2 for g and 30m for z1 in Equation (XII).

  hp=( 25.46m/s )22(9.81m/ s 2)+1293.26m30m=33.03m+1263.26m=1296.29m

Substitute 9.81m/s2 for g, 999.1kg/m3 for ρ, 18L/s for Q and 1296.29m for hp in Equation (XIII).

  P=(18L/s)(999.1kg/m3)(9.81m/s2)(1296.29m)=(18L/s)( 10 3m31L)(999.1kg/m3)(9.81m/s2)(1296.29m)(1kW 10 3kg m 2/ s 3)=(0.018)(12705.15)kW=228.69kW

Conclusion:

The required pumping head is 1296.29m.

The pumping power required to maintain the flow is 228.69kW.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Q1: Determine the length, angle of contact, and width of a 9.75 mm thick leather belt required to transmit 15 kW from a motor running at 900 r.p.m. The diameter of the driving pulley of the motor is 300 mm. The driven pulley runs at 300 r.p.m. and the distance between the centers of two pulleys is 3 meters. The density of the leather is 1000 kg/m³. The maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction between the leather and pulley is 0.3. Assume open belt drive.
5. A 15 kW and 1200 r.p.m. motor drives a compressor at 300 r.p.m. through a pair of spur gears having 20° stub teeth. The centre to centre distance between the shafts is 400 mm. The motor pinion is made of forged steel having an allowable static stress as 210 MPa, while the gear is made of cast steel having allowable static stress as 140 MPa. Assuming that the drive operates 8 to 10 hours per day under light shock conditions, find from the standpoint of strength, 1. Module; 2. Face width and 3. Number of teeth and pitch circle diameter of each gear. Check the gears thus designed from the consideration of wear. The surface endurance limit may be taken as 700 MPa. [Ans. m = 6 mm; b= 60 mm; Tp=24; T=96; Dp = 144mm; DG = 576 mm]
4. G A micarta pinion rotating at 1200 r.p.m. is to transmit 1 kW to a cast iron gear at a speed of 192 r.p.m. Assuming a starting overload of 20% and using 20° full depth involute teeth, determine the module, number of teeth on the pinion and gear and face width. Take allowable static strength for micarta as 40 MPa and for cast iron as 53 MPa. Check the pair in wear.

Chapter 8 Solutions

Fluid Mechanics: Fundamentals and Applications

Ch. 8 - What is hydraulic diameter? How is it defined?...Ch. 8 - Shown here is a cool picture of water being...Ch. 8 - What fluid property is responsible for the...Ch. 8 - In the fully developed region of flow in a...Ch. 8 - Someone claims that the volume flow rate in a...Ch. 8 - Someone claims that the average velocity in a...Ch. 8 - Someone claims that the shear stress at the center...Ch. 8 - Someone claims that in fully developed turbulent...Ch. 8 - How does the wall shear stress w , vary along the...Ch. 8 - How is the friction factor for flow in a pipe...Ch. 8 - Discuss whether fully developed pipe flow is one-,...Ch. 8 - Consider fully developed flow in a circular pipe...Ch. 8 - Consider fully developed laminar how in a...Ch. 8 - Explain why the friction factor is independent of...Ch. 8 - Consider laminar flow of air in a circular pipe...Ch. 8 - Consider fully developed laminar flow in a...Ch. 8 - How is head loss related to pressure loss? For a...Ch. 8 - What is turbulent viscosity? What caused it?Ch. 8 - What is the physical mechanism that causes the...Ch. 8 - The head toss for a certain circular pipe is given...Ch. 8 - The velocity profile for the fully developed...Ch. 8 - Water at 15°C (p = 999.1 kg/m3 and = 1.138 × 10-3...Ch. 8 - Water at 70F passes through...Ch. 8 - Heated air at 1 atm and 100F is to be transported...Ch. 8 - In fully developed laminar flow in a circular...Ch. 8 - The velocity profile in fully developed laminar...Ch. 8 - Repeat Prob. 8-36 for a pipe of inner radius 7 cm.Ch. 8 - Water at 10C (p = 999.7 kg/m3 and = 1.307 ×...Ch. 8 - Consider laminar flow of a fluid through a square...Ch. 8 - Repeat Prob. 8-39 for tribulent flow in smooth...Ch. 8 - Air enters a 10-m-long section of a rectangular...Ch. 8 - Consider an air solar collector that is 1 m wide...Ch. 8 - Oil with p = 876 kg/m3 and = 0.24 kg/m.s is...Ch. 8 - Glycenii at 40 C with p = l22 kg/m3 and = 0.27...Ch. 8 - Air at 1 atm and 60 F is flowing through a 1 ft ×...Ch. 8 - Oil with a density of 850 kg/m3 and kinematic...Ch. 8 - In an air heating system, heated air at 40 C and...Ch. 8 - Glycerin at 40 C with p = 1252 kg/m3 and = 0.27...Ch. 8 - Liquid ammonia at 20 C is flowing through a...Ch. 8 - Consider the fully developed flow of glycerin at...Ch. 8 - The velocity profile for a steady laminar flow in...Ch. 8 - The generalized Bernoulli equation for unsteady...Ch. 8 - What is minor loss in pipe flow? How is the minor...Ch. 8 - Define equivalent length for minor loss in pipe...Ch. 8 - The effect of rounding of a pipe inlet on the loss...Ch. 8 - The effect of rounding of a pipe exit on the loss...Ch. 8 - Which has a greater minor loss coefficient during...Ch. 8 - A piping system involves sharp turns, and thus...Ch. 8 - During a retrofitting project of a fluid flow...Ch. 8 - A horizontal pipe has an abrupt expansion from...Ch. 8 - Consider flow from a water reservoir through a...Ch. 8 - Repeat Prob. 8-62 for a slightly rounded entrance...Ch. 8 - Water is to be withdrawn from an 8-m-high water...Ch. 8 - A piping system equipped with a pump is operating...Ch. 8 - Water is pumped from a large lower reservoir to a...Ch. 8 - For a piping system, define the system curve, the...Ch. 8 - Prob. 68CPCh. 8 - Consider two identical 2-m-high open tanks tilled...Ch. 8 - A piping system involves two pipes of different...Ch. 8 - A piping system involves two pipes of different...Ch. 8 - A piping system involves two pipes of identical...Ch. 8 - Water at 15 C is drained from a large reservoir...Ch. 8 - Prob. 74PCh. 8 - The water needs of a small farm are to be met by...Ch. 8 - Prob. 76EPCh. 8 - A 2.4-m-diameter tank is initially filled with...Ch. 8 - A 3-m-diameter tank is initially filled with water...Ch. 8 - Reconsider Prob. 8-78. In order to drain the tank...Ch. 8 - Gasoline (p = 680 kg/m3 and v = 4.29 × 10-7 m2/s)...Ch. 8 - Prob. 81EPCh. 8 - Oil at 20 C is flowing through a vertical glass...Ch. 8 - Prob. 83PCh. 8 - A 4-in-high cylindrical tank having a...Ch. 8 - A fanner is to pump water at 70 F from a river to...Ch. 8 - A water tank tilled with solar-heated vater at 4OC...Ch. 8 - Two water reservoirs A and B are connected to each...Ch. 8 - Prob. 89PCh. 8 - A certain pail of cast iron piping of a water...Ch. 8 - Repeat Prob. 8-91 assuming pipe A has a...Ch. 8 - Prob. 93PCh. 8 - Repeat Prob. 8-93 for cast lion pipes of the same...Ch. 8 - Water is transported by gravity through a...Ch. 8 - Water to a residential area is transported at a...Ch. 8 - In large buildings, hot water in a water tank is...Ch. 8 - Prob. 99PCh. 8 - Two pipes of identical length and material are...Ch. 8 - What are the primary considerations when selecting...Ch. 8 - What is the difference between laser Doppler...Ch. 8 - Prob. 103CPCh. 8 - Prob. 104CPCh. 8 - Explain how flow rate is measured with...Ch. 8 - Prob. 106CPCh. 8 - Prob. 107CPCh. 8 - Prob. 108CPCh. 8 - A 15-L kerosene tank (p = 820 kg/m3) is filled...Ch. 8 - Prob. 110PCh. 8 - Prob. 111PCh. 8 - Prob. 112PCh. 8 - Prob. 113PCh. 8 - Prob. 114EPCh. 8 - Prob. 115EPCh. 8 - Prob. 116PCh. 8 - A Venturi meter equipped with a differential...Ch. 8 - Prob. 119PCh. 8 - Prob. 120PCh. 8 - Prob. 121PCh. 8 - Prob. 122EPCh. 8 - Prob. 123PCh. 8 - The flow rate of water at 20°C (p = 998 kg/m3 and ...Ch. 8 - Prob. 125PCh. 8 - Prob. 126PCh. 8 - Prob. 127PCh. 8 - The conical container with a thin horizontal tube...Ch. 8 - Prob. 129PCh. 8 - The compressed air requirements of a manufacturing...Ch. 8 - A house built on a riverside is to be cooled iii...Ch. 8 - The velocity profile in fully developed lamina,...Ch. 8 - Prob. 133PCh. 8 - Two pipes of identical diameter and material are...Ch. 8 - Prob. 135PCh. 8 - Shell-and-tube heat exchangers with hundred of...Ch. 8 - Water at 15 C is to be dischaged froiti a...Ch. 8 - Consider flow front a reservoir through a...Ch. 8 - A pipelme ihat Eransports oil ai 4OC at a iate of...Ch. 8 - Repeat Prob. 8-140 for hot-water flow of a...Ch. 8 - Prob. 142PCh. 8 - Prob. 145EPCh. 8 - Prob. 146EPCh. 8 - In a hydroelectric power plant. water at 20°C is...Ch. 8 - Prob. 148PCh. 8 - Prob. 152PCh. 8 - The water at 20 C in a l0-m-diameter, 2-m-high...Ch. 8 - Prob. 155PCh. 8 - Find the total volume flow rate leaving a tank...Ch. 8 - Prob. 158PCh. 8 - Water is siphoned from a reservoir open to the...Ch. 8 - It is a well-known fact that Roman aqueduct...Ch. 8 - In a piping system, what is used to control the...Ch. 8 - Prob. 163PCh. 8 - Prob. 164PCh. 8 - Prob. 165PCh. 8 - Consider laminar flow of water in a...Ch. 8 - Water at 10 C flows in a 1.2-cm-diameter pipe at a...Ch. 8 - Engine oil at 20 C flows in a 15-cm-diamcter pipe...Ch. 8 - Prob. 169PCh. 8 - Watet flows in a I 5-cm-diameter pipe a, a...Ch. 8 - The pressure drop for a given flow is determined...Ch. 8 - Prob. 172PCh. 8 - Air at 1 atm and 25 C flows in a 4-cm-diameter...Ch. 8 - Hot combustion 8ases approximated as air at I atm...Ch. 8 - Air at 1 aim and 40 C flows in a 8-cm-diameter...Ch. 8 - The valve in a piping system cause a 3.1 in head...Ch. 8 - A water flow system involves a 180 return bend...Ch. 8 - Air flows in an 8-cm-diameter, 33-m-long pipe at a...Ch. 8 - Consider a pipe that branches out into two...Ch. 8 - Prob. 182PCh. 8 - Prob. 183PCh. 8 - Prob. 184PCh. 8 - Prob. 185PCh. 8 - Prob. 186PCh. 8 - Design an experiment to measure the viscosity of...Ch. 8 - During a camping trip you notice that water is...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Physics 33 - Fluid Statics (1 of 10) Pressure in a Fluid; Author: Michel van Biezen;https://www.youtube.com/watch?v=mzjlAla3H1Q;License: Standard YouTube License, CC-BY