To determine The pressure at the beginning of the exhaust system Explanation Write the expression for the cross sectional area of the pipe. A = π 4 D 2 (I). Here, diameter of the pipe is D . Write the expression for the velocity of the exhaust air. V = Q A (II) Here, the flow rate of the air is Q . Write the expression for the ideal gas equation. p V = m R T p ( V m ) = R T ρ = p R T (III) Write the equation for Reynolds number. Re = ρ V D μ (IV) Here, the Reynolds number is Re , the velocity of the fluid is V and the dynamics viscosity of fluid is μ . Write the expression for the major head loss ( h L ) m a j o r . ( h L ) m a j o r = f l V 2 2 g D (V) Here, friction factor is f , length of the pipe is l , velocity is v , acceleration due to gravity is g , and diameter of the pipe is D . Write the expression for the minor losses. ( h L ) minor = n ( K Lelbows V 2 2 g ) + K L muffler V 2 2 g ∑ K L V 2 2 2 g = ( n K e l b o w s + K L muffler ) V 2 2 g (VI) Write the expression for the energy balance equation for the given system including the major and minor losses. p 1 γ + V 1 2 2 g + z 1 = p 2 γ + V 2 2 2 g + z 2 + ∑ K L V 2 2 2 g + f l V 2 2 g (VII) Here, the pressure at point 1 is p 1 , the velocity at point 1 is V 1 , the elevation at point 1 is z 1 , the pressure at point 2 is p 2 , the velocity at point 2 is V 2 , the elevation at point 2 is z 2 , loss coefficient is K L , friction factor is f , and length of the pipe is l . Consider Point (1) and points (2) are same height from the datum line. z 1 = z 2 (VIII) Since the exhaust flows to atmosphere at outlet of the pipe so the pressure at the outlet is zero. p 2 = 0 Consider the steady state condition, so the initial velocity must be equal to final velocity of the outlet. V 1 = V 2 = V (IX) Use equation (VIII) and (IX) and substitute 0 for p 2 in equation (I). p 1 ρ g = ∑ K L V 2 2 2 g + f l V 2 2 g (X) Conclusion: Substitute 0.125 ft for D in equation (I). A = π 4 ( 0.125 ft ) 2 = 0.01227 ft 2 Substitute 0.1 ft 3 /s for Q and 0.01227 ft 2 for A in equation (II) V = ( 0.1 ft 3 / s ) ( 0.01227 ft 2 ) = 8.1487 ft/s Substitute 14.7 lb/in . 2 for p , 1716 ft ⋅ lb slug°R for R , and 250 ° F for T in equation (III) ρ = 14

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 8.5, Problem 65P

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The pressure at the beginning of the exhaust system

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Chapter 8.4, Problem 64P

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

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