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 3, Problem 135P

If the rate of rotational speed of the 3-tube system shown in Fig. P3-135 is ω = 10 rad/s, determine the water heights in each tube leg. At what rotational speed will the middle tube be completely empty?

Expert Solution & Answer
Check Mark
To determine

The water height in each tube.

The speed at which the middle limb is completely empty.

Answer to Problem 135P

The height of water in left tube is 23.15cm.

The height of water in right tube is 19.08cm

The height of water in middle tube is 2.77cm.

The angular speed at which the middle limb is completely empty is 15.07rad/s.

Explanation of Solution

Given information:

The rotational speed of the system is 10rad/s, the height of water in the right tube before rotation is 15cm, the bottom length between middle and right tube is 10cm and the bottom length between left and middle tube is 20cm.

Write the expression for the water level rises in the left limb.

  (L1+L22+2x3)=(L1+L22x)+12gVL2   ...... (I)

Here, the distance of the left limb from the axis is L1, the distance of the right limb from the axis is L2, the axis that is located at 23 distance from the midpoint of the system is x, the acceleration due to gravity is g and the velocity in the left limb is VL.

Write the expression for the velocity in the left limb.

  VL=ωL1   ...... (II)

Here, the angular speed is ω.

Write the expression for the rise of liquid in the left limb.

  hL=(L1+L22+2x3)   ...... (III)

Here, the rise in the left limb is hL.

Write the expression for the water level rises in the right limb.

  hR=(L1+L22+x3)   ...... (IV)

Here, the rise of water in the right limb is hR.

Write the expression for the rise of water in middle limb.

  hm=L1+L22x   ...... (V)

Here, the rise of water in the middle limb is hm.

Write the expression for the angular velocity at which the water height in the middle limb is zero.

  ω=4g( h L h m )R2   ...... (VI)

Here, the distance between the center and the left limb is R.

Calculation:

Substitute 20cm for L1 and 10rad/s for ω in Equation (II).

  VL=(10rad/s)×(20cm)=(10rad/s)×(20cm× 1m 100cm)=2m/s

Substitute 20cm for L1, 10cm for L2, 9.81m/s2 for g and 2m/s for VL in Equation (I).

  ( 20cm+10cm2+ 2x3)=( 20cm+10cm2x)+1( 2×9.81m/ s 2 )(2m/s)2[(15cm× 1m 100cm)+2x3]=[(15cm× 1m 100cm)x]+(0.2038m)(0.15m+ 2x3)=(0.15mx)+0.2038mx=0.1223m

Substitute 20cm for L1, 10cm for L2 and 0.1223m for x in Equation (III).

  hL=( 20cm+10cm2+ 2×0.1223m3)=(15cm+( 0.08152m× 100cm 1m ))=23.15cm

Substitute 20cm for L1, 10cm for L2 and 0.1223m for x in Equation (IV).

  hR=( 20cm+10cm2+ 0.1223m3)=(15cm+( 0.04077m× 100cm 1m ))=19.08cm

Substitute 20cm for L1, 10cm for L2 and 0.1223m for x in Equation (V).

  hm=( 20cm+10cm20.1223m)=(15cm( 0.1223m× 100cm 1m ))=2.77cm

Substitute 9.81m/s2 for g, 23.15cm for hL, 0cm for hm and 20cm for R in Equation (VI).

  ω= 4×( 9.81m/ s 2 )×( 23.15cm0cm ) ( 20cm ) 2 = ( 39.24m/ s 2 )×( ( 23.15cm )×( 1m 100cm ) ) ( 20cm×( 1m 100cm ) ) 2 =227.10rad/s=15.07rad/s

Conclusion:

The height of water in left tube is 23.15cm.

The height of water in right tube is 19.08cm

The height of water in middle tube is 2.77cm.

The angular speed at which the middle limb is completely empty is 15.07rad/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
The water level in the 1.8 m high and 1 m diameter cylindrical tank in the figure is 1.4 m. If this tank is rotated around its own axis at what speed will the axial depth be zero? (In other words, what is the number of revolutions at which a dry area will begin to form at the bottom of the tank?) Take the gravitational acceleration as 10 m / s2 and π as 3.
For the system shown in figure, find the time required to fill the cylindrical tank (D-60cm) if, V₁-3m/s, D₁=2cm, V₂-5m/s, D₂-6cm, and V3-7.2m/s, D3-5cm. 02 1) h=1.2m 3 (2)
A gate having a cross-sectional area of quarter circle is used to control the water flow of a reservoir as shown below. The quarter circle has a radius of R = 1 m, and its weight is 40 × 103 N per unit width (into the page). A pin is used to connect the gate with a vertical wall. At which height h of water does the gate open. Assume that water temperature is 20°, and use the standard value of the gravitational acceleration. If needed, use the table for area and centroid attached to the end of this homework. Water Pin 1 m Gate P 1 m

Chapter 3 Solutions

Fluid Mechanics: Fundamentals and Applications

Ch. 3 - Show that 1kgf/cm2=14.223psi .Ch. 3 - The pressure in a water line is 1500 kPa. What is...Ch. 3 - Blood pressure is usually measured by rapping a...Ch. 3 - The maximum blood pressure in the upper arm of a...Ch. 3 - Consider a 1.73-m-tall man standing vertically in...Ch. 3 - A manometer is used to measure the air pressure in...Ch. 3 - The water in a tank is pressurized by air, and the...Ch. 3 - Determine the atmospheric pressure at a location...Ch. 3 - The gagepressure in a liquid at a depth of 2.5 m...Ch. 3 - The absolute pressure in water at a depth of 8 m...Ch. 3 - A 180-Ibm man has a total foot imprint area of 68...Ch. 3 - Consider a 55-kg woman who has a total foot...Ch. 3 - A vacuum gage connected to a tank reads 45 kPa at...Ch. 3 - The piston of a vertical piston-cylinder device...Ch. 3 - The vacuum pressure of a condenser is given to be...Ch. 3 - Water from a reservoir is raised in a vertical...Ch. 3 - The barometer of a mountain hiker reads 980 mbars...Ch. 3 - Determine the pressure exerted on a diver at 15 m...Ch. 3 - A gas is contained in a vertical, frictionless...Ch. 3 - The variation of pressure P in a gas with density ...Ch. 3 - Both a gage and a manometer are attached to a gas...Ch. 3 - The system shown in the figure is used to...Ch. 3 - The manometer shown in the figure is designed to...Ch. 3 - A manometer containing ( =850kg/m3 ) attached to a...Ch. 3 - A mercury ( =13,600kg/m3 ) is connected to an air...Ch. 3 - Repeat Prob. 3-37 for a differential mercury...Ch. 3 - Consider a U-tube whose arms are open to the...Ch. 3 - The hydraulic lift in a car repair shop has an...Ch. 3 - Consider a double-fluid manometer attached to an...Ch. 3 - The pressure in a natural gas pipeline is measured...Ch. 3 - Repeat Prob. 3-42E by replacing air by oil with a...Ch. 3 - The gage pressure of the air in the tank shown in...Ch. 3 - Repeat Prob. 3-44 for a gage pressure of 40 kPa.Ch. 3 - The 500-kg load on the hydraulic lift show in Fig....Ch. 3 - Pressure is often given in terms of a liquid...Ch. 3 - Freshwater and seamier flowing in parallel...Ch. 3 - Repeat Prob. 3-48 by replacing the air with oil...Ch. 3 - The pressure difference between an oil pipe and...Ch. 3 - Consider the system shown in Fig. P3-51. If a...Ch. 3 - There is water at a height of 1 m in the rube open...Ch. 3 - Prob. 53PCh. 3 - A simple experiment has long been used to...Ch. 3 - A multifluid container is connected to a U-tube....Ch. 3 - A hydraulic lift is to be used to lift a 2500 kg...Ch. 3 - On a day in which the local atmospheric pressure...Ch. 3 - A U-tube manometer is used to measure the pressure...Ch. 3 - Define the resultant hydrostatic force acting on a...Ch. 3 - You may have noticed that dams are much thicker at...Ch. 3 - Someone claims that she can determine the...Ch. 3 - A submersed horizontal flat plate is suspended in...Ch. 3 - Consider a submerged curved surface. Explain how...Ch. 3 - Consider a submersed curved surface. Explain how...Ch. 3 - Consider a circular surface subjected to...Ch. 3 - Consider a 200-ft-high, dam filled to capacity....Ch. 3 - A cylindrical tank is folly filled with water...Ch. 3 - Consider a 8-m-long, 8-m-wide, and 2-m-high...Ch. 3 - Consider a heavy car submerged in water in a lake...Ch. 3 - A room the lower level of a cruise ship has a...Ch. 3 - The water side of the wall of a 70-m-long dam is a...Ch. 3 - A water trough of semicircular cross section of...Ch. 3 - Determine the resultant force acting on the...Ch. 3 - A 6-m-high, 5-m-wide rectangular plate blocks the...Ch. 3 - The flow of water from a reservoir is controlled...Ch. 3 - Repeat Prob. 3-76E for a water height of 6 ft.Ch. 3 - For a gate width of 2 m into the paper (Fig....Ch. 3 - A long, solid cylinder of radius 2 ft hinged at...Ch. 3 - An open settling tank shown in the figure contains...Ch. 3 - From Prob. 3-80, knowing that the density of the...Ch. 3 - The two sides of a V-shaped water trough are...Ch. 3 - Repeat Prob. 3-82 for the case of a partially...Ch. 3 - The bowl shown in the figure (the white volume) is...Ch. 3 - A triangular-shaped gate is hinged at point A, as...Ch. 3 - Gate AB ( 0.60.9m ) is located at the bottom of a...Ch. 3 - Find the force applied by support BC to the gate...Ch. 3 - A concrete block is attached to the sate as shown....Ch. 3 - A 4-m-long quarter-circular gate of radius 3 m and...Ch. 3 - Repeat Prob. 3-90 for a radius of 2 m for the...Ch. 3 - What is buoyant force? What causes it? What is the...Ch. 3 - Prob. 93CPCh. 3 - Consider two 5-cm-diaineter spherical balls-one...Ch. 3 - Prob. 95CPCh. 3 - Consider two identical spherical bails submerged...Ch. 3 - Prob. 97PCh. 3 - The hull of a boat has a volume of 180 m3, and the...Ch. 3 - The density of a liquid is to be determined by an...Ch. 3 - Prob. 100PCh. 3 - It is estimated that 90 percent of an iceberg’s...Ch. 3 - One of the common procedures in fitness programs...Ch. 3 - The weight of a body is usually measured by...Ch. 3 - Under what conditions can a moving body of fluid...Ch. 3 - Consider a vertical cylindrical container...Ch. 3 - Consider two identical glasses of water, one...Ch. 3 - Consider a glass of water. Compare the water...Ch. 3 - A water tank is being towed by a truck on a level...Ch. 3 - Consider two water tanks filled with water. The...Ch. 3 - Prob. 111PCh. 3 - The bottom quarter of a vertical cylindrical tank...Ch. 3 - A 3-m-diameter, 7-m-long cylindrical tank is...Ch. 3 - A 30-cm-diameter, 90-cm-high vertical cylindrical...Ch. 3 - A fish tank that contains 60-cm-high water is...Ch. 3 - A15-ft-long, 6-ft-high rectangular tank open to...Ch. 3 - Consider a tank of rectangular cross-section...Ch. 3 - A 3-ft-diameter vertical cylindrical lank open to...Ch. 3 - Milk with a density of 1020 kg/m3 is transported...Ch. 3 - Prob. 120PCh. 3 - The distance between the centers of the two arms...Ch. 3 - A 1.2-m-diameter, 3-m-high scaled vertical...Ch. 3 - A 4-m-diameter vertical cylindrical milk tank...Ch. 3 - An 8-ft-long tank open to the atmosphere initially...Ch. 3 - Prob. 126PCh. 3 - Prob. 127PCh. 3 - Prob. 128PCh. 3 - Two vertical and connected cylindrical tanks of...Ch. 3 - The U-tube shown the figure subjected to an...Ch. 3 - Prob. 131EPCh. 3 - An air-conditioning system requires a 34-m-long...Ch. 3 - Determine the pressure exerted on the surface of a...Ch. 3 - A vertical, frictionless piston-cylinder device...Ch. 3 - If the rate of rotational speed of the 3-tube...Ch. 3 - The average atmospheric pressure on earth is...Ch. 3 - Prob. 137PCh. 3 - Prob. 139PCh. 3 - The basic barometer can be used as an...Ch. 3 - The lower half of a 12-m-high cylindrical...Ch. 3 - Prob. 142PCh. 3 - A pressure cooker cooks a lot faster than an...Ch. 3 - Prob. 144PCh. 3 - An oil pipeline and a 1.3-m3 rigid air tank are...Ch. 3 - A 20-cm-diameter vertical cylindrical vessel is...Ch. 3 - Prob. 148PCh. 3 - A gasoline line is connected to a pressure gage...Ch. 3 - Prob. 151PCh. 3 - Prob. 152EPCh. 3 - Consider a U-tube filled with mercury as shown in...Ch. 3 - The variation of pressure with density in a thick...Ch. 3 - A 3-m-high. 5-m-wide rectangular gale is hinged al...Ch. 3 - Prob. 156PCh. 3 - A semicircular 40-ft-diameter tunnel is to be...Ch. 3 - A 30-ton. 4-m-diameter hemispherical dome on a...Ch. 3 - The water in a 25-m-deep reservoir is kept inside...Ch. 3 - A 5-m-long, 4-m-high tank contains 2.5-m-deep...Ch. 3 - The density of a floating body can be determined...Ch. 3 - A raft is made using a number of logs with 25 cm...Ch. 3 - A prismatic timber is at equilibrium in a liquid,...Ch. 3 - The cylindrical lank containing water accelerates...Ch. 3 - A 30-cm-diameter. 100-cm-hish vertical cylindrical...Ch. 3 - The 280-ke, 6-m-wide rectangular gate shown in Fig...Ch. 3 - Prob. 168PCh. 3 - Determine the vertical force applied by water on...Ch. 3 - Prob. 170PCh. 3 - In order to keep the cone-shaped plus closed as...Ch. 3 - The gage pressure in a pipe is measured by a...Ch. 3 - Prob. 173PCh. 3 - Prob. 174PCh. 3 - The atmospheric pressure in a location is measured...Ch. 3 - Prob. 176PCh. 3 - Prob. 177PCh. 3 - Consider the vertical rectangular wall of a water...Ch. 3 - Prob. 179PCh. 3 - Prob. 180PCh. 3 - Prob. 181PCh. 3 - Prob. 182PCh. 3 - Prob. 183PCh. 3 - Prob. 184PCh. 3 - Consider a 6-m-diameter spherical sate holding a...Ch. 3 - Prob. 186PCh. 3 - Prob. 187PCh. 3 - Prob. 188PCh. 3 - Prob. 189PCh. 3 - Prob. 190PCh. 3 - Prob. 191PCh. 3 - Prob. 192PCh. 3 - Shoes are to be designed to enable people of up to...Ch. 3 - The volume of a rock is to be determined without...Ch. 3 - Compare fee vortex with forced vortex according to...Ch. 3 - The density of stainless steel is about 8000 kg/m3...
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