To determine Determine the relation between the differential reading on the manometer and the applied gage pressure. Explanation Show the schematic diagram of the U tube manometer as in Figure (1). Express the gage pressure when the valve is closed and the pressure is applied. P g − γ H g Δ h = P a Δ h = P g − P a γ H g (I) Here, gage pressures are P g and P a respectively, difference in level is Δ h and the specific weight of the mercury is γ H g . Consider the temperature of the trapped air remains constant. Express the relation for the isothermal compression of the trapped air. P ρ = constant [ 1 ρ ] P = constant ∀ P = constant Here, density of air is ρ and specific volume of air is ∀ . Express the relation for isothermal compression for the process. P i ∀ i = P f ∀ f (II) Here, the initial and final specific volumes of the air is ∀ i and ∀ f respectively and the absolute pressure of the air at initial and final condition is P i and P f respectively. Express the initial specific volume of the air. ∀ i = A i h i Here, area of the tube is A i . Express the final specific volume of the air. ∀ f = A i [ h i − Δ h 2 ] Conclusion: Substitute P a t m for P i and ( P a + P a t m ) for P f in Equation (II). P a t m ∀ i = ( P a + P a t m ) ∀ f (III) Substitute A i h i for ∀ i and A i [ h i − Δ h 2 ] for ∀ f in Equation (III). P a t m ( A i h i ) = ( P a + P a t m ) { A i [ h i − Δ h 2 ] } P a = P a t m [ h i h i − Δ h 2 − 1 ] Substitute P a t m [ h i h i − Δ h 2 − 1 ] for P a in Equation (I). Δ h = P g − P a t m [ h i h i − Δ h 2 − 1 ] γ H g = 1 γ H g { P g − P a t m [ h i h i − Δ h 2 − 1 ] } = P g γ H g − P a t m γ H g [ 2 h i 2 h i − Δ h ] + [ P a t m γ H g ] Δ h = P g γ H g − P a t m γ H g [ 2 h i 2 h i − Δ h ] + [ P a t m γ H g ] 2 Δ h h i − ( Δ h ) 2 = 2 P g h i γ H g − P g Δ h γ H g − 2 h i P a t m γ H g + 2 P a t m h i γ H g − P a t m Δ h γ H g ( Δ h ) 2 − [ 2 h i + P g γ H g + P a t m γ H g ] ( Δ h ) + 2 P g h i γ H g = 0 (IV) Obtain the roots of the quadratic equation in Equation (IV)

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 2.6, Problem 52P

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Chapter 2.6, Problem 51P

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Chapter 2 Solutions

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

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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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