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

Textbook Question
Book Icon
Chapter 8, Problem 73P

Water at 15 ° C is drained from a large reservoir using two horizontal plastic pipes connected in series. The first pipe is 13 m long and has a 10-cm diameter, while the second pipe is 35 m long and has a 5-cm diameter. The water level in the reservoir is 18 in above the centerline of the pipe. The pipe entrance is sharp-edged, and the contraction between the two pipes is sudden. Neglecting the effect of the kinetic energy correction factor, determine the discharge rate of water from the reservoir.

Expert Solution & Answer
Check Mark
To determine

The discharge rate of water from reservoir.

Answer to Problem 73P

The discharge rate of water from reservoir is 0.0206(m3/s).

Explanation of Solution

Given information:

Reservoir is drained at 15°C, length of first pipe is 13m, diameter of first pipe is 10cm, length of second pipe is 35m, diameter of second pipe is 5cm, and water level is 18m above the centerline of pipe. The entrance in the pipe is sharp edged and contraction between the pipes is sudden. Neglect the effect of kinetic energy correction factor.

Write the expression of datum head.

  z1=α2V222g+hL   ....... (I)

Here, kinetic energy correction factor at point 2 is α2, velocity at point 2 is V2, head loss at point 2 is hL, and the acceleration due to gravity is g.

Write the expression of total head loss.

  hL=hL,major+hL,minor   ....... (II)

Here, the major head loss is hL,major and minor head loss is hL,minor.

Write the expression for major head loss.

  hL,major=(fL1D+KL,entrance)V122g

Here, the friction factor is f, the length of pipe 1 is L1, the diameter of pipe 1 is D, the loss coefficient at entrance is KL,entrance, the velocity of water at point 1 is V1, and the acceleration due to gravity is g.

Write the expression of minor head loss.

  hL,minor=(fL2d+KL,contraction)V222g

Here, the friction factor is f, the length of pipe 2 is L2, the diameter of pipe 2 is d, the loss coefficient at contraction is KL,contraction, the velocity of water at point 2 is V2, and the acceleration due to gravity is g.

Substitute (fL1D+KL,entrance)V122g for hL,major and (fL2d+KL,contraction)V222g for hL,minor in Equation (II).

  hL=(fL1D+KL,entrance)V122g+(fL2d+KL,contraction)V222g   ....... (III)

Write the expression for discharge through the pipe.

  Q=A1V1   ....... (IV)

Here, the area of flow of fluid is A1 and the velocity of flow in pipe 1 is V1.

Write the expression of area of flow of fluid from pipe 1.

  A1=(π4)×D2

Here, the diameter of pipe 1 is D.

Write the expression of area of flow of fluid from pipe 2.

  A2=(π4)×d2

Here, the diameter of pipe 2 is d.

Substitute (π4)×D2 for A1 in Equation (IV).

  Q=(π4)×D2×V1   ....... (V)

Write the expression of continuity equation.

  A1V1=A2V2   ....... (VI)

Here, the flow area of pipe 1 is A1, the flow velocity of water in pipe 1 is V1, the flow area of pipe 2 is A2, the flow velocity of water in pipe 2 is V2.

Substitute π4D2 for A1 and π4d2 for A2 in Equation (VI)

  π4D2×V1=π4d2×V2V2=( D d)2×V   ....... (VII)

Write the expression of squire of ratio of diameter of pipe.

  dr=d2D2   ....... (VIII)

Here, the diameter of pipe 2 is d and the diameter of pipe 1 is D.

Calculation:

Substitute 5cm for d and 10cm for D in Equation (VII).

  V2=( 10cm 5cm)2×V1=(2)2×V1=4×V1

Substitute, 18m for z1, 1 for α2, 9.81m/s2 for g and 4×V1 for V2 in Equation (I).

  18m=1× ( 4× V 1 )22×( 9.81m/ s 2 )+hLhL=18m0.815×V12( m/ s 2 )=18m0.815×V12( s 2/m)

Substitute 5cm for d and 10cm for D in Equation (VIII).

  dr= ( 5cm )2 ( 10cm )2=0.25

Refer Table 8-4 "Loss coefficient of KL for various pipe" to find the loss coefficient corresponding to 0.25 is 0.46 at contraction and 0.5 at entrance.

Refer Table 8-2 "Equivalence roughness values for new commercial pipe" to find the roughness value as 0 corresponding to plastic pipe and friction factor as 0.0119 corresponding to ε/D=0.

Substitute, 18m0.815×V12(s2/m) for hL

  0.0119 for f, 13m for L1, 10cm for D, 4×V1 for V2

  9.81m/s2 for g, 35m for L2, 5cm for d, 0.5 for KL,entrance and 0.46 for KL,contraction in Equation (III).

  18m0.815×V12( s 2/m)=[( 0.0119× 13m 10cm +0.5) V 1 2 2×9.81m/ s 2 +( 0.0119× 35m 5cm +0.46) 4× V 1 2 2×9.81m/ s 2 ]18m0.815×V12( s 2/m)=[( 0.155m ( 10cm )×( 1m 100cm ) +0.5)×0.05× V 1 2( s 2 /m )+( 0.4165m ( 5cm )×( 1m 100cm ) +0.46)×0.2× V 1 2( s 2 /m )]18m0.815×V12( s 2/m)=0.1×V12( s 2/m)+1.7×V12( s 2/m)18m=2.615×V12( s 2/m)

  V12=6.88( m 2/ s 2)V1=( 6.88( m 2 / s 2 ))=2.63(m/s)

Substitute 10cm for D, 2.63(m/s) for V1 in Equation (V).

  Q=(π4)×(10cm)2×2.63(m/s)=(π4)×(10cm×( 1m 100cm ))2×2.63(m/s)=2.06×(1 100m2)×(m/s)=0.0206( m 3/s)

Conclusion:

The discharge rate of water from reservoir is 0.0206(m3/s).

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
A pump increases the pressure of water from 100 kPa to 1.2 MPa at a rate of 0.5 m3 /min. The inlet and outlet diameters are identical and there is no change in elevation across the pump. If the efficiency of the pump is 77 percent, the power supplied to the pump is (a) 11.9 kW (b) 12.6 kW (c) 13.3 kW (d ) 14.1 kW (e) 15.5 kW
A horizontal water pipe diameter 15 cm converges to 7.5 cm diameter. If the pressures at the two sections are 4 kg/cm2, and 1.5 kg/cm2 respectively, calculate the flow rate of water.
Using the situation below, how would I determine the net resultant force exerted on the reducer by the water? In this situation, water is flowing horizontally in a pipe that has a diameter of 25cm. This water is flowing at 8 m/s and at 300 kPa gage it enters a 90 degree bend reducing section. This bend reducing section is connected to a vertical pipe that has a diamater of 15cm. Moreover, the inlet of the bend is 45 cm above the exit. Here, fricition and gravity are negligible and the momentum flux correction factor is 1.04.

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
Fluid Mechanics - Viscosity and Shear Strain Rate in 9 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=_0aaRDAdPTY;License: Standard youtube license