Explanation Write the expression of horizontal component of the headwater hydrostatic force ( F H H ) . F H H = γ y c A F H H = γ ( h H 2 ) ( b × h H ) F H H = γ b h H 2 2 (I) Here, specific weight is γ , area of the triangle is A , base is b and height is h H . Write the expression of vertical component of the headwater hydrostatic force ( F H V ) . F H V = γ V ′ + γ V ″ F H V = γ ( l b h ) ′ + γ ( ( 1 2 b h ) l ) ′ ′ (II) Here, length is l , breadth is b and height is h . Write the expression of horizontal component of the tailwater hydrostatic force ( F T H ) . F T H = γ y c A F T H = γ ( h T 2 ) ( b × h T ) F T H = γ b h T 2 2 (III) Here, specific weight is γ , area of the triangle is A , base is b and height is h T . Write the expression of vertical component of the tailwater hydrostatic force ( F T V ) . F T V = γ V F T V = γ ( 1 2 b h T ) l (IV) Here, length is l , breadth is b and height is h T . Write the expression of the dam weight at section 1 ( W 1 ) . W 1 = γ c V 1 W 1 = γ c ( 1 2 b h ) l (V) Here, specific weight of concrete is γ c , length is l , breadth is b and height is h . Write the expression of the dam weight at section 2 ( W 2 ) . W 2 = γ c V 2 W 2 = γ c ( l b h ) (VI) Write the expression of the dam weight at section 3 ( W 3 ) . W 3 = γ 3 V 3 W 3 = γ c ( 1 2 b h ) l (VII) Write the expression to obtain the total force ( F ) . F = F H V + F T V + W 1 + W 2 + W 3 (VIII) Write the net force causing the dam to move downstream ( F n e t ) . F n e t = F H H − F T H (IX) Conclusion: Draw the free body diagram of the Altus dam as in Figure (1). Substitute 62.4 lb / ft 3 for γ , 1 ft for b and 87 ft for h H in Equation (I). F H H = ( 62.4 lb / ft 3 ) ( 1 2 ) ( 1 ft ) ( 87 ft ) 2 F H H = 236200 lb Obtain the y -coordinate of the line of action of the force. Y p = 2 3 ( 87 ft ) = 58 ft Substitute 62.4 lb / ft 3 for γ , 1 ft for l ′ , 7 ft for b ′ , 8 ft for h ′ , 1 ft for l ″ , 8 ft for b ″ and ( 87 − 7 ) ft for h ″ in Equation (II). F H V = ( 62.4 lb / ft 3 ) ( 1 ft ) ( 7 ft ) ( 8 ft ) + ( 62.4 lb / ft 3 ) ( 1 ft ) ( 8 ft ) ( 87 − 7 ) ft 2 = 23460 lb Obtain the location X p of F H V

8th Edition

ISBN: 9781119571490

Author: GERHART

Publisher: WILEY

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Chapter 2.8, Problem 98P

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Chapter 2.8, Problem 97P

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Chapter 2 Solutions

FUNDAMENTALS OF FLUID MECHANICS

Ch. 2.3 - Prob. 1P Ch. 2.3 - The deepest known spot in the oceans is the...Ch. 2.3 - A closed tank is partially filled with glycerin....Ch. 2.3 - A 3-m-diameter vertical cylindrical tank is filled...Ch. 2.3 - Blood pressure is usually given as a ratio of the...Ch. 2.3 - An unknown immiscible liquid seeps into the bottom...Ch. 2.3 - A 30-ft-high downspout of a house is clogged at...Ch. 2.3 - How high a column of SAE 30 oil would be required...Ch. 2.3 - Bathyscaphes are capable of submerging to great...Ch. 2.3 - The deepest known spot in the oceans is the...

Ch. 2.3 - A submarine submerges by admitting seawater (S =...Ch. 2.3 - Determine the pressure at the bottom of an open...Ch. 2.3 - In a certain liquid at rest, measurements of the...Ch. 2.3 - Because of elevation differences, the water...Ch. 2.3 - Under normal conditions the temperature of the...Ch. 2.3 - Often young children drink milk (ρ = 1030 kg/m3)...Ch. 2.3 - (See The Wide World of Fluids article titled...Ch. 2.4 - What would be the barometric pressure reading, in...Ch. 2.4 - Denver, Colorado, is called the “mile-high city”...Ch. 2.4 - Prob. 20P Ch. 2.4 - Pikes Peak near Denver, Colorado, has an elevation...Ch. 2.4 - Equation 2.12 provides the relationship between...Ch. 2.4 - As shown in Fig. 2.6 for the U.S. standard...Ch. 2.4 - (See The Wide World of Fluids article titled...Ch. 2.5 - On a given day, a barometer at the base of the...Ch. 2.5 - Aneroid barometers can be used to measure changes...Ch. 2.5 - Bourdon gages (see Video V2.4 and Fig. 2.13) are...Ch. 2.5 - On the suction side of a pump, a Bourdon pressure...Ch. 2.5 - A Bourdon pressure gage attached to the outside of...Ch. 2.6 - Obtain a photograph/image of a situation in which...Ch. 2.6 - A U-tube manometer is used to check the pressure...Ch. 2.6 - A barometric pressure of 29.4 in. 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Ch. 2.8 - A tank contains 6 in. of oil (S = 0.82) above 6...Ch. 2.8 - A structure is attached to the ocean floor as...Ch. 2.8 - Concrete is poured into the forms as shown in Fig....Ch. 2.8 - A long, vertical wall separates seawater from...Ch. 2.8 - Forms used to make a concrete basement wall are...Ch. 2.8 - While building a high, tapered concrete wall,...Ch. 2.8 - A homogeneous, 4-ft-wide, 8-ft-long rectangular...Ch. 2.8 - A gate having the shape shown in Fig. P2.88 is...Ch. 2.8 - A pump supplies water under pressure to a large...Ch. 2.8 - Prob. 90P Ch. 2.8 - Prob. 91P Ch. 2.8 - The dam shown in Fig. P2.92 is 200 ft long and is...Ch. 2.8 - Prob. 93P Ch. 2.8 - Figure P2.94 is a representation of the Keswick...Ch. 2.8 - The Keswick dam in Problem 2.94 is made of...Ch. 2.8 - The Keswick dam in Problem 2.94 is made of...Ch. 2.8 - Prob. 97P Ch. 2.8 - Prob. 98P Ch. 2.8 - Find the magnitude and location of the net...Ch. 2.8 - Prob. 100P Ch. 2.8 - Find the total vertical force on the cylinder...Ch. 2.8 - A 3-m-wide, 8-m-high rectangular gate is located...Ch. 2.8 - A gate having the cross section shown in Fig....Ch. 2.8 - The massless, 4-ft-wide gate shown in Fig. P2.104...Ch. 2.8 - A 200-lb homogeneous gate 10 ft wide and 5 ft long...Ch. 2.8 - An open tank has a vertical partition and on one...Ch. 2.8 - Prob. 107P Ch. 2.8 - A 4-ft by 3-ft massless rectangular gate is used...Ch. 2.8 - A thin 4-ft-wide, right-angle gate with negligible...Ch. 2.8 - The closed vessel of Fig. P2.110 contains water...Ch. 2.8 - (See The Wide World of Fluids article titled “The...Ch. 2.10 - Obtain a photograph/image of a situation in which...Ch. 2.10 - Prob. 113P Ch. 2.10 - Prob. 114P Ch. 2.10 - Figure P2.115 shows a cross section of a submersed...Ch. 2.10 - The container shown in Fig. P2.116 has circular...Ch. 2.10 - The 18-ft-long lightweight gate of Fig. P2.117 is...Ch. 2.10 - The air pressure in the top of the 2-liter pop...Ch. 2.10 - In drilling for oil in the Gulf of Mexico, some...Ch. 2.10 - Hoover Dam (see Video 2.5) is the highest...Ch. 2.10 - A plug in the bottom of a pressurized tank is...Ch. 2.10 - The homogeneous gate shown in Fig. P2.122...Ch. 2.10 - The concrete (specific weight = 150 lb/ft3)...Ch. 2.10 - Prob. 124P Ch. 2.10 - Find the magnitude, direction, and location of the...Ch. 2.10 - A 10-m-long log is stuck against a dam, as shown...Ch. 2.10 - Prob. 127P Ch. 2.10 - Prob. 128P Ch. 2.10 - Prob. 129P Ch. 2.10 - Prob. 130P Ch. 2.10 - Prob. 131P Ch. 2.11 - Prob. 132P Ch. 2.11 - An iceberg (specific gravity 0.917) floats in the...Ch. 2.11 - Prob. 134P Ch. 2.11 - Prob. 135P Ch. 2.11 - Prob. 136P Ch. 2.11 - Prob. 137P Ch. 2.11 - Prob. 138P Ch. 2.11 - Estimate the minimum water depth needed to float a...Ch. 2.11 - Prob. 140P Ch. 2.11 - Prob. 141P Ch. 2.11 - Prob. 142P Ch. 2.11 - Prob. 143P Ch. 2.11 - A solid cylindrical pine (S = 0.50) spar buoy has...Ch. 2.11 - Prob. 145P Ch. 2.11 - Prob. 146P Ch. 2.11 - Prob. 147P Ch. 2.11 - A submarine is modeled as a cylinder with a length...Ch. 2.12 - Prob. 149P Ch. 2.12 - Prob. 150P Ch. 2.12 - Prob. 151P Ch. 2.12 - Prob. 152P Ch. 2.12 - Prob. 153P Ch. 2.12 - The cylinder in Fig. P2.154 accelerates to the...Ch. 2.12 - A closed cylindrical tank that is 8 ft in diameter...Ch. 2.12 - The cart shown in Fig. P2.156 measures 10.0 cm...Ch. 2.12 - The U-tube manometer in Fig. P2.157 is used to...Ch. 2.12 - Prob. 158P Ch. 2.12 - An open 1-m-diameter tank contains water at a...Ch. 2.12 - Prob. 160P Ch. 2.12 - Prob. 161P Ch. 2.12 - Prob. 162P Ch. 2.12 - Prob. 163P

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