a. Explanation Given data: Refer figure P13.66 Formula used: Write the expression for Bernoulli’s equation. p 1 + 1 2 ρ v 1 2 + ρ g y 1 = p 2 + 1 2 ρ v 2 2 + ρ g y 2 (1) Here, p 1 , p 2 is the pressure, ρ is the density, g is the acceleration due to gravity, y 1 , y 2 is the height, and v 1 , v 2 is the speed. Write the expression for continuity equation. v 1 A 1 = v 2 A 2 (2) Here, v 1 , v 2 is the speed, and A 1 , A 2 is the area. Write the expression for pressure. p 2 = p 0 + ρ g d (3) Here, p 2 , p 0 is the pressure, ρ is the density, g is the acceleration, and d is the height. Explanation: The height is, 10 cm = 0.1 m { ∵ 1 cm = 10 − 2 m } The radius of the second part is, 1 2 cm = 0 .5 cm = 0 .5 × 10 − 2 m The radius of the first part, 2.0 mm 2 = 1.0 mm = 1.0 × 10 − 3 m { ∵ 1 mm = 10 − 3 m } The area of cross section is, A = π r 2 (4) For area of the second part, Substitute 0 .5 × 10 − 2 m for r , A 2 = π ( 0 .5 × 10 − 2 m ) 2 = 7.85 × 10 − 5 m 2 For area of the first part, Substitute 1.0 × 10 − 3 m for r in equation (4), A 1 = π ( 1.0 × 10 − 3 m ) 2 = 3.14 × 10 − 6 m 2 Rearrange equation (3) to solve for pressure difference. p 2 − p 0 = ρ g d Substitute p 1 for p 0 in the equation, p 2 − p 1 = ρ liquid g d (5) Rearrange equation (2) to solve for v 1 . v 1 = v 2 A 2 A 1 . (6) The height y 1 is same as y 2 . Substitute y 1 for y 2 in equation (1), p 1 + 1 2 ρ v 1 2 + ρ g y 1 = p 2 + 1 2 ρ v 2 2 + ρ g y 1 p 1 + 1 2 ρ v 1 2 + ρ g y 1 − ρ g y 1 = p 2 + 1 2 ρ v 2 2 p 1 + 1 2 ρ v 1 2 = p 2 + 1 2 ρ v 2 2 Rearrange the above to solve for p 2 − p 1 . p 2 − p 1 = 1 2 ρ v 1 2 − 1 2 ρ v 2 2 Substitute equation (4) in the above equation, ρ liquid g d = 1 2 ρ v 1 2 − 1 2 ρ v 2 2 (7) Substitute equation (5) in the above equation, ρ liquid g d = 1 2 ρ ( v 2 A 2 A 1 ) 2 − 1 2 ρ v 2 2 ρ liquid g d = 1 2 ρ v 2 2 A 2 2 − 1 2 ρ v 2 2 A 1 2 A 1 2 ρ liquid g d = 1 2 ρ v 2 2 ( A 2 2 − A 1 2 ) A 1 2 A 1 2 ρ liquid g d = 1 2 ρ v 2 2 ( A 2 2 − A 1 2 ) 2 A 1 2 ρ liquid g d = ρ v 2 2 ( A 2 2 − A 1 2 ) v 2 = A 1 2 ρ liquid g d ρ ( A 2 2 − A 1 2 ) (8) From table 13 b. To determine The volume flow rate.

16th Edition

ISBN: 9781323515303

Author: Knight

Publisher: PEARSON C

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Question

Chapter 13, Problem 66GP

To determine

The air speeds v1 and v2 at points 1 and 2.

To determine

The volume flow rate.

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Chapter 13, Problem 65GP

Chapter 13, Problem 67GP

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