Loose Leaf For Fluid Mechanics
Loose Leaf For Fluid Mechanics
8th Edition
ISBN: 9781259169922
Author: White, Frank M.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.159P
To determine

(a)

The formula for change in height of the tube.

Expert Solution
Check Mark

Answer to Problem 2.159P

The formula for change in height of the tube is Δhcentre=13Ω2R2g.

Explanation of Solution

Given information:

The depth of water is 20cm, the angular velocity is 120r/min.

Write the expression for total displacement between outer and center menisci.

htotal=v22g ……. (I)

Here, total displacement is htotal, velocity is v and the acceleration due to gravity is g.

Write the expression for velocity.

v=ΩR ……. (II)

Here, angular velocity is Ω and the radius is R.

Substitute ΩR for v in Equation (I).

htotal= ( ΩR )22g=Ω2R22g ……. (III)

Write the expression for change in height.

Δhouter=Δhcentre2 …… (IV)

Here, the change in height of outer half is Δhouter and the change in height of the center tube is Δhcentre.

Write the expression for rise of water in outer leg.

Δhouter=13htotal ……. (V)

Substitute Ω2R22g for htotal in Equation (V).

Δhouter=13Ω2R22g=16Ω2R2g

Substitute 16Ω2R2g for Δhouter in Equation (IV).

16Ω2R2g=Δh centre2Δhcentre=2×16Ω2R2gΔhcentre=13Ω2R2g

Conclusion:

The formula for change in height of the tube is Δhcentre=13Ω2R2g.

To determine

(b)

The height in each tube.

Expert Solution
Check Mark

Answer to Problem 2.159P

The height of water in outer tube is 0.0268m.

The height of water in center tube is 0.0536m.

Explanation of Solution

Given information:

The depth of water is 20cm, the angular velocity is 120r/min and the radius is 10cm.

Write the expression for displacement in outer tube.

Δhouter=16Ω2R2g ……. (VI)

Here, displacement in outer tube is Δhouter, acceleration due to gravity is g, angular velocity is Ω and the radius is R.

Write the expression for displacement of water in central tube.

Δhcentre=13Ω2R2g ……. (VII)

Here, displacement of water height in center tube is Δhcentre.

Calculation:

Substitute 120r/min for Ω, 10cm for R and 9.8m/s2 for g in Equation (VI).

Δhouter=16 ( ( 120r/ min ) )2 ( ( 10cm ) )29.8 m/s 2=16 ( ( 120r/ min )( 2π 60 radians ) )2 ( ( 10cm )( 1m 100cm ) )29.8 m/s 2=0.0268m

Substitute 120r/min for Ω, 10cm for R and 9.8m/s2 for g in Equation (VII).

Δhcenter=13 ( ( 120r/ min ) )2 ( ( 10cm ) )29.8 m/s 2=13 ( ( 120r/ min )( 2π 60 radians ) )2 ( ( 10cm )( 1m 100cm ) )29.8 m/s 2=0.0536m

Conclusion:

The height of water in outer tube is 0.0268m.

The height of water in center tube is 0.0536m.

The negative sign shows that the height in center tube is decreased.

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Chapter 2 Solutions

Loose Leaf For Fluid Mechanics

Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - Prob. 2.14PCh. 2 - Prob. 2.15PCh. 2 - Prob. 2.16PCh. 2 - Prob. 2.17PCh. 2 - The system in Fig. P2.18 is at 20°C. If...Ch. 2 - Prob. 2.19PCh. 2 - The hydraulic jack in Fig. P2.20 is filled with...Ch. 2 - At 20°C gage A reads 350 kPa absolute. What is the...Ch. 2 - The fuel gage for a gasoline tank in a car reads...Ch. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - Prob. 2.26PCh. 2 - P2.27 Conduct an experiment to illustrate...Ch. 2 - Prob. 2.28PCh. 2 - Prob. 2.29PCh. 2 - Prob. 2.30PCh. 2 - In Fig. P2.31 all fluids arc at 20°C. Determine...Ch. 2 - For the inverted manometer of Fig. P2.32, all...Ch. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Water flows upward in a pipe slanted at 30°, as in...Ch. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - If the pressure in container A in Fig. P2.38 is...Ch. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - P2.41 The system in Fig. P2.41 is at 20°C....Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - In Fig. P2.46 both ends of the manometer are open...Ch. 2 - Prob. 2.47PCh. 2 - The system in Fig. P2.4H is open to 1 atm on the...Ch. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Gate AB in Fig. P2.51 is 1.2 m long and 0.8 m into...Ch. 2 - Example 2.5 calculated the force on plate AB and...Ch. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Gate AB in Fig. P2.55 is 5 ft wide into the paper,...Ch. 2 - Prob. 2.56PCh. 2 - Prob. 2.57PCh. 2 - Prob. 2.58PCh. 2 - Gate AB has length L and width b into the paper,...Ch. 2 - Prob. 2.60PCh. 2 - Gale AB in Fig. P2.61 is homogeneous mass of 180...Ch. 2 - Gale AB in Fig. P2.62 is 15 ft long and 8 ft wide...Ch. 2 - The tank in Fig. P2.63 has a 4-cm-diameter plug at...Ch. 2 - Prob. 2.64PCh. 2 - Prob. 2.65PCh. 2 - Prob. 2.66PCh. 2 - Prob. 2.67PCh. 2 - P2.68 Isosceles triangle gate AB in Fig. P2.68 is...Ch. 2 - P2.69 Consider the slanted plate AB of length L in...Ch. 2 - Prob. 2.70PCh. 2 - Prob. 2.71PCh. 2 - Prob. 2.72PCh. 2 - P2.73 Gate AB is 5 ft wide into the paper and...Ch. 2 - Prob. 2.74PCh. 2 - Prob. 2.75PCh. 2 - Prob. 2.76PCh. 2 - P2.77 The circular gate ABC in Fig. P2.77 has l-m...Ch. 2 - Prob. 2.78PCh. 2 - Prob. 2.79PCh. 2 - Prob. 2.80PCh. 2 - Prob. 2.81PCh. 2 - Prob. 2.82PCh. 2 - Prob. 2.83PCh. 2 - Prob. 2.84PCh. 2 - P2.85 Compute the horizontal and vertical...Ch. 2 - Prob. 2.86PCh. 2 - The bottle of champagne (SG = 0.96) in Fig. P2.87...Ch. 2 - Prob. 2.88PCh. 2 - Prob. 2.89PCh. 2 - The lank in Fig. P2.90 is 120 cm long into the...Ch. 2 - The hemispherical dome in Fig. P2.91 weighs 30 kN...Ch. 2 - A 4-m-diameter water lank consists of two half...Ch. 2 - Prob. 2.93PCh. 2 - Prob. 2.94PCh. 2 - Prob. 2.95PCh. 2 - Prob. 2.96PCh. 2 - Prob. 2.97PCh. 2 - Prob. 2.98PCh. 2 - The mega-magnum cylinder in Fig. P2.99 has a...Ch. 2 - Pressurized water fills the tank in Fig, P2.100....Ch. 2 - Prob. 2.101PCh. 2 - Prob. 2.102PCh. 2 - Prob. 2.103PCh. 2 - Prob. 2.104PCh. 2 - P2.105 it is said that Archimedes discovered the...Ch. 2 - Prob. 2.106PCh. 2 - Prob. 2.107PCh. 2 - P2.108 A 7-cm-diameter solid aluminum ball (SG =...Ch. 2 - Prob. 2.109PCh. 2 - Prob. 2.110PCh. 2 - P2.111 A solid wooden cone (SG = 0.729) floats in...Ch. 2 - The uniform 5-m-long round wooden rod in Fig....Ch. 2 - Prob. 2.113PCh. 2 - Prob. 2.114PCh. 2 - P2.115 The 2-in by 2-in by 12-ft spar buoy from...Ch. 2 - Prob. 2.116PCh. 2 - The solid sphere in Fig. P2.117 is iron ( SG7.9 )....Ch. 2 - Prob. 2.118PCh. 2 - Prob. 2.119PCh. 2 - Prob. 2.120PCh. 2 - Prob. 2.121PCh. 2 - Prob. 2.122PCh. 2 - Prob. 2.123PCh. 2 - Prob. 2.124PCh. 2 - Prob. 2.125PCh. 2 - Prob. 2.126PCh. 2 - Prob. 2.127PCh. 2 - Prob. 2.128PCh. 2 - Prob. 2.129PCh. 2 - Prob. 2.130PCh. 2 - Prob. 2.131PCh. 2 - Prob. 2.132PCh. 2 - Prob. 2.133PCh. 2 - Prob. 2.134PCh. 2 - P2.135 Consider a homogeneous right circular...Ch. 2 - Prob. 2.136PCh. 2 - Prob. 2.137PCh. 2 - Prob. 2.138PCh. 2 - P2.139 The tank of liquid in Kg. 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