To determine The pressure at the throat of a Venturi meter. Explanation Write the expression for the ideal gas equation. ρ = P 1 R T 1 (I) Here, the density of the fluid is ρ , the pressure in the pipe is P 1 , the temperature of the air is T 1 and the characteristics gas constant is R . Write the expression for the discharge. Q = y ρ g (II) Here, the acceleration due to gravity is g , the rate is y and the discharge in the pipe is Q . Write the equation for velocity. Re = ρ V D μ (III) Here, the Reynolds number is Re , the dynamics viscosity of fluid is μ , the velocity of the fluid is V and the density of the fluid is ρ . Write the equation for velocity. V = 4 Q π D 2 (IV) Here, the velocity in the pipe is V and the diameter of the pipe is D . Write the expression for flow rate. Q = C π v ( d 0 ) 2 4 2 ( P 1 − P 2 ) ρ ( 1 − ( d 0 d 1 ) 4 ) (V) Here, the coefficient of volume is C v , the first diameter of the pipe is d 1 , the second diameter of the pipe is d 0 and the pressure drop is P 1 − P 2 . Conclusion: Substitute 60 psia for P 1 , 1716 ft ⋅ lb / slug ° R for R , 200 ° F for T 1 in Equation (I). ρ = 60 psia ( 1716 ft ⋅ lb / slug ° R ) ( 200 ° F ) = 60 psia ( 1 lb / in 2 1 psia ) ( 1716 ft ⋅ lb / slug ° R ) ( 200 ° F+460 ) ° R = 60 lb / in 2 ( 1716 ft ⋅ lb / slug ° R ) ( 660 ° R ) = 60 lb / in 2 ( 1132560 ft ⋅ lb / slug ) ρ = 0.000052977 slug / ft ⋅ in 2 ( 1 in 2 0.0069444 ft 2 ) = 0.00762878 slug / ft 3 Substitute 0.52 lb / s for y , 0.00762878 slug / ft 3 for ρ and 32.2 ft / s 2 for g in Equation (II). Q = 0.52 lb / s 0.00762878 slug / ft 3 × 32.2 ft / s 2 = 0.52 lb / s 0.2456465 slug / ft 2 ⋅ s 2 = 2.11686 lb ⋅ ft 2 ⋅ s / slug ( 1 slug ⋅ ft / s 2 1 lb ) = 2.11686 ft 3 / s Substitute 4 in for D and 2.11686 ft 3 / s for Q in Equation (IV). V = 4 ( 2.11686 ft 3 / s ) π ( 4 in ) 2 = 8.46744 ft 3 / s π ( 4 in ( 1 ft 12 in ) ) 2 = 2.6952 ft 3 / s 0.11112 ft 2 = 24.1788 ft / s Refer the Table B-3, “Physical Properties of Air at Standard Atmospheric Pressure (BG/EE Units) to obtain the value of the dynamic viscosity is 4.49 × 10 − 7 lb ⋅ s / ft 2 corresponding to 200 ° F

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ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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Chapter 8.6, Problem 127P

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The pressure at the throat of a Venturi meter.

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Chapter 8.6, Problem 126P

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