To determine The minimum air pressure within the container that will open the hatch Explanation Draw the schematic diagram of the hatch as shown in figure (1). Write the expression for the area of the Hatch. A = π 4 d 2 (I) Here, diameter of the hatch is d . Write the expression for the centroid of the hatch. h c = 10 m + ( D 2 sin θ ) (II) Here, the angle at which the hatch is pivoted is θ . Write the expression for the hydrostatic force on the hatch. F R = γ h c A (III) Here, specific weight of the water is γ w , vertical height of the centroid of the hatch is h , and area of the hatch is A . Write the expression for the moment of inertia of the hatch. I x x = π 4 R 4 (IV) Here, radius of the hatch is R . Write the expression for the centroid distance from the free surface along the axis of hatch. y c = ( 10 m sin θ ) + D 2 (V) Write the expression for the center of pressure. y p = I x x y c A + y c (VI) Draw the free body diagram of the hatch as shown in figure (2). Apply the principle of moment about the hinged point H . ∑ M H = 0 F × ( y p − 10 m sin θ ) − p a A ( D 2 ) = 0 (VII) Here, pressure of the air acting on the other side of the hatch is p A . Conclusion: Substitute 2 m for D in equation (I). A = π 4 ( 2 m ) 2 = 3.14 m 2 Substitute 2 m for D and 30 ° for θ in equation (II) h c = 10 m + ( ( 2 m ) 2 sin 30 ° ) = 10 + 0.5 = 10.5 m Substitute 10.1 kN m 3 for γ , 10.5 m for h c , and 3

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ISBN: 9781119571490

Author: GERHART

Publisher: WILEY

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Chapter 2.8, Problem 82P

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The minimum air pressure within the container that will open the hatch

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Chapter 2.8, Problem 81P

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Chapter 2 Solutions

FUNDAMENTALS OF FLUID MECHANICS

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Hg corresponds...Ch. 2.6 - For an atmospheric pressure of 101 kPa (abs)...Ch. 2.6 - The closed tank of Fig. P.2.34 is filled with...Ch. 2.6 - A mercury manometer is connected to a large...Ch. 2.6 - The U-tube manometer shown in Fig. P2.36 has two...Ch. 2.6 - A U-tube manometer is connected to a closed tank...Ch. 2.6 - The container shown in Fig. P2.38 holds 60 °F...Ch. 2.6 - A closed cylindrical tank filled with water has a...Ch. 2.6 - Two pipes are connected by a manometer as shown in...Ch. 2.6 - Find the percentage difference in the readings of...Ch. 2.6 - A U-tube manometer is connected to a closed tank...Ch. 2.6 - For the inclined-tube manometer of Fig. P2.43, the...Ch. 2.6 - A flowrate measuring device is installed in a...Ch. 2.6 - The sensitivity Sen of the micromanometer shown in...Ch. 2.6 - The cylindrical tank with hemispherical ends shown...Ch. 2.6 - Determine the elevation difference. Δh, between...Ch. 2.6 - What is the specific gravity of the liquid in the...Ch. 2.6 - For the configuration shown in Fig. P2.49 what...Ch. 2.6 - The manometer shown in Fig. P2.50 has an air...Ch. 2.6 - The U-tube manometer shown in Fig. P2.51 has legs...Ch. 2.6 - Both ends of the U-tube mercury manometer of Fig....Ch. 2.6 - The inverted U-tube manometer of Fig. P2.53...Ch. 2.6 - An inverted U-tube manometer containing oil (SG =...Ch. 2.6 - The sensitivity Sen of the manometer shown in Fig....Ch. 2.6 - In Fig. P2.56 pipe A contains gasoline (SG = 0.7),...Ch. 2.6 - The mercury manometer of Fig. P2.57 indicates a...Ch. 2.6 - Consider the cistern manometer shown in Fig....Ch. 2.6 - Prob. 59P Ch. 2.6 - Prob. 60P Ch. 2.6 - Determine the new differential reading along the...Ch. 2.6 - Prob. 62P Ch. 2.6 - Determine the ratio of areas, A1/A2, of the two...Ch. 2.6 - Prob. 64P Ch. 2.6 - Prob. 65P Ch. 2.6 - An inverted hollow cylinder is pushed into the...Ch. 2.8 - Obtain a photograph/image of a situation in which...Ch. 2.8 - The basic elements of a hydraulic press are shown...Ch. 2.8 - The hydraulic cylinder shown in Fig. P2.69, with a...Ch. 2.8 - A Bourdon gage (see Fig. 2.13 and Video V2.4) is...Ch. 2.8 - A bottle jack allows an average person to lift one...Ch. 2.8 - Suction is often used in manufacturing processes...Ch. 2.8 - A piston having a cross-sectional area of 0.07 m2...Ch. 2.8 - Prob. 74P Ch. 2.8 - The container shown in Fig. P2.75 has square cross...Ch. 2.8 - Find the weight W needed to hold the wall shown in...Ch. 2.8 - Determine the magnitude and direction of the force...Ch. 2.8 - An automobile has just dropped into a river. 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