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

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 8, Problem 148P
To determine

The percentage increase in net power output.

Expert Solution & Answer
Check Mark

Answer to Problem 148P

The percentage increase in net power output is 14.30%.

Explanation of Solution

Given information:

The diameter of the cast iron pipe is 0.35m and the length of the cast iron pipe is 200m. The head loss during pump is 140m and the density of water at 20°C is 998kg/m3. The viscosity of water at 20°C is 0.001002kg/ms and the combined turbine efficiency is 80%. The diameter of the pipe is tripled in order to reduced the pipe loss.

Write the expression for energy equation for a control volume.

  P1ρg+α1V122g+z1+hpump=P2ρg+α2V222g+z2+hturbine+hL  ...... (I)

Here, the pressure at point 1 is P1, the pressure at point 2 is P2, the height at 1 is z1, the height at 2 is z2, the velocity at point 1 is V1, the velocity at point 2 is V2,the head loss due to pump is hpump, the head loss due to turbine is hturbine, the kinetic energy correction factor at point 1 is α1, the kinetic energy correction factor at point 2, acceleration due to gravity is g, the density of fluid is ρ and the head loss in the pipe is hL.

Write the expression for average velocity.

  V=4V˙π(D)2....... (II)

Here, the volume flow rate is V˙, the diameter of the pipe is D and the relative velocity is V.

Write the expression for Reynolds number for flow in pipe.

  Re=ρVDμ...... (III)

Here, the Reynolds number for flow in pipe is ReA and the density of fluid is ρ and

Write the expression for Colebrook equation for pipe A.

  1f=2log(ε/D3.7+2.51Ref)...... (IV)

Here, the relative velocity through the pipe is ε/D and the friction factor of the pipe f.

Write the expression for the head loss in pipe.

  hL=fLV22gD..... (V)

Here, the head loss in the pipe is hL, the friction factor in pipe is fA, the length of the pipe is LA and the velocity ion the pipe is LB.

Write the expression for percentage increase in net power output.

  %increase=hturbinehturbine,ehturbine,e×100  ...... (VI)

Calculation:

Substitute Patm for P1, 0 for V1, Patm for P2, 140m for hpump and 0 for V2 in Equation (I).

  PEρg+α1(0)2g+0+140m=P atmρg+α2(0)2g+0+hturbine+hL140m=hturbine+hLhturbine+hL=140m....... (VII)

Substitute 0.35m for D and 0.55m3/s for V˙ in Equation (II).

  V=4( 0.55 m 3 /s )π ( 0.35m )2=2.2 m 3/s1.099×0.35m2=5.7194m/s

Substitute 998kg/m3 for ρ, 1.002×103kg/ms for μ and 0.35m for D in Equation (III).

  Re=( 998 kg/ m 3 )( 5.7194m/s )( 0.35m)1.002× 10 3kg/ms=1997.786kg/ms1.002× 10 3kg/ms=1993798.822

Refer the Table-3.1, "Roughness height for certain common Pipe materials" to obtain the value of the roughness height 0.26×103m corresponding through cast iron pipe.

Substitute 0.35m for D, 1993798.822 for Re and 0.26×103m for ε in Equation (IV).

  1f=2log( 0.26× 10 3 m/ 0.35m 3.7+ 2.51 1993798.822 f )=2log( 7.422857× 10 4 3.7+ 1.258× 10 6 f )=2log(2.006× 10 4+ 1.258× 10 6 f )=0.0185

Substitute 5.71m/s for D, 0.35m for D, 200m for L, 9.81m/s2 for g and 0.0185 for f in Equation (V).

  hL=( 0.0185)( 200m) ( 5.71m/s )22( 9.81m/ s 2 )( 0.35m)=120.635 m 3/s6.865 m 2/s=17.5724m

Substitute 17.5724m for hL in Equation (VII).

  hturbine,e+17.5724m=140mhturbine,e=140m-17.5724mhturbine,e=122.427m

Substitute (0.35×3)m for D and 0.55m3/s for V˙ in Equation (II).

  V=4( 0.55 m 3 /s )π ( 3×0.35m )2=2.2 m 3/s0.38484m2=0.6354m/s

Substitute 998kg/m3 for ρ, 1.002×103kg/ms for μ and (0.35×3)m for D in Equation (III).

  Re=( 998 kg/ m 3 )( 0.6354m/s )( 0.35m×3)1.002× 10 3kg/ms=665.835kg/ms1.002× 10 3kg/ms=664506.646

Substitute (0.35×3)m for D, 664506.646 for Re and 0.26×103m for ε in Equation (IV).

  1f=2log( 0.26× 10 3 m/ ( 0.35×3 )m 3.7+ 2.51 664506.646× f )=2log( 2.4722857× 10 4 3.7+ 3.777× 10 6 f )=2log(6.6924× 10 5+ 3.777× 10 6 f )=0.0155

Substitute 0.6354m/s for V, (0.35×3)m for D, 200m for L, 9.81m/s2 for g and 0.0155 for f in Equation (V).

  hL=( 0.0155)( 200m) ( 0.6354m/s )22( 9.81m/ s 2 )( 0.35×3m)=1.2515 m 3/s20.601 m 2/s=0.06074m

Substitute 0.06074m for hL in Equation (VII).

  hturbine+0.06074m=140mhturbine=140m0.06074mhturbine=139.9392m

Substitute 122.427m for hturbine,e and 139.9392m for hturbine in Equation (VI).

  %increase=139.9392m122.427m122.427m×100=17.5122m122.427m×100=14.30%

Conclusion:

The percentage increase in net power output is 14.30%.

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
The loss coefficients for the pipe shown is: up to A it is 0.8, from A to B it is 1.2, from B to C it is 0.8, from C to D it is 2.2. Estimate the flow rate and the pressures at A, B, C, and D. The elevations are shown. al 10m al. 3m O P₁ B U Solution: 1. The energy equation can be simplified to 02₁-22= 1 el. 12 m P2 D 3 cm dia. 4. Pressure at A, PA= m; 5. Pressure at B, PB= m; 10 28 2g o The total energy loss occurred through this system is calculated as: h= o Relationship between Upipe and Vexit 2. Thus, velocity in the pipe is Upipe 3. Calculate the flow rate Q= -m; = is:-Vexit= m³/s; m/s; Upipe i kPa; (energy equation from surface to A) kPa; (energy equation from surface to B) Upipe 2g
Water at a temperature of 25 C is pumped through the 100-mm-diameter commercial steel pipe over a distance of 500 m Use the equation 1.11 /D -1.8 log 6.9 (Figure 1) Re 3.7
The diameter of the smooth pipes used in the pumping system in the lower figure is 150 mm and its total length is 80 m. In this system, there are four elbows with a loss coefficient of 0.2. It's lost its coefficients are 0.5 for the inlet to the pipe, 0.7 for the valve and 1 for the inlet to the tank. z2-z1=15 m, above manometric pressure if the flow of water pumped into the tank is 50 L/s and the overall efficiency of the pump is %84 find his height and strength. Take the viscosity of water is 0.001 kg / m.s

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
Surface Finish Measurement - Skidded VS. Skidless Surface Roughness Measurement; Author: Mitutoyo America Corporation;https://www.youtube.com/watch?v=X7jCTIwVs80;License: Standard Youtube License