Fluid Mechanics Fundamentals And Applications
Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
bartleby

Videos

Textbook Question
Book Icon
Chapter 12, Problem 109P

Air enters a 15-cm-diameter adiabatic duct with inlet conditions of V 1  =  150   m / s ,   T 1  =  500   K ,   a n d   P 1  = 200  k P a . For an average friction factor of 0.014, determine the duct length from the inlet where the inlet velocity doubles. Also determine the pressure drop along that section of the duct.

Expert Solution & Answer
Check Mark
To determine

The duct length when velocity is doubled and the pressure drop along the length of duct.

Answer to Problem 109P

The duct length for velocity to be doubled is 39.583m.

The pressure drop along the length of duct is 106.728kPa.

Explanation of Solution

Given information:

The diameter of pipe is 15cm, inlet velocity is 150m/s, inlet temperature is 500K, inlet pressure is 200kPa, average friction factor is 0.014.

Expression for inlet Mach number

   Ma1=V1kRT1     ...... (I)

Here, inlet velocity is V1, gas constant is R, specific heat ratio is k, inlet temperature is T1.

Expression for length required for sonic flow for inlet condition

   fL1*Dh=1Ma12kMa12+k+12kln(k+1)Ma122+(k1)Ma12     ...... (II)

Here, friction factor is f, diameter of pipe is Dh, inlet sonic length is L1*.

Expression for pressure drop

   ΔP=P1P2     ...... (III)

Here, inlet pressure is P1.

Expression for length required for velocity double

   L=( f L 1 * D h f L 2 * D h )(f D h )     ...... (IV)

Here, length of pipe is L, outlet sonic length is L2*.

Calculation:

Refer to Table-A-1 “Molar mass, gas constant, and ideal gas specific heat of some substances” to obtain gas constant of air as 287J/kgK and specific heat ratio as 1.4

Substitute 150m/s for V1, 500K for T1, 1.4 for k and 287J/kgK for R in Equation (I).

   Ma1=150m/s 1.4( 287J/ kgK )500K=150m/s 200900J/ kg × 1 kg m 2 / kg s 2 1J/ kg =150m/s448.2186m/s=0.33465

Refer to Table-A-15 “Rayleigh flow function for an ideal gas with k=1.4 ” at Mach number 0.33465 to obtain ratio of pressure temperature and velocity.

Relation of velocity at initial state and sonic state

   V1V*=0.362553     ...... (V)

Here, inlet velocity at sonic state is V*.

Substitute 150m/s for V1 in Equation (VI).

   150m/sV*=0.362553V*=150m/s0.362553V*=413.732m/s

Relation of pressure at initial state and sonic state

   P1P*=3.237351     ...... (VI)

Here, inlet pressure at sonic state is P*.

Substitute 200kPa for P1 in Equation (VI).

   200kPaP*=3.237351P*=200kPa3.237351P*=61.778kPa

Substitute 0.33465 for Ma1, 1.4 for k in Equation (II).

   fL1*Dh=1 ( 0.33465 )21.4 ( 0.33465 )2+1.4+12×1.4ln( 1.4+1) ( 0.33465 )22+( 1.41) ( 0.33465 )2=1 ( 0.33465 )21.4 ( 0.33465 )2+67ln( 2.4) ( 0.33465 )22+( 0.4) ( 0.33465 )2=3.9245

Substitute 300m/s for V2 and 413.732m/s for V* in the ratio V2V*.

   V2V*=300m/s413.732m/s=0.7251×1m/s1m/s=0.7251

Refer to Table-A-16 “Fanno flow function for an ideal gas with k=1.4 ” at V2V* as 0.7251 to obtain Mach number at exit as 0.693, fL2*Dh as 0.23 and pressure ratio as 1.5098.

Relation of pressure at exit and sonic state

   P2P*=1.5098     ...... (VII)

Substitute 61.778kPa for P* in Equation (VII).

   P261.778kPa=1.5098P2=61.778kPa×1.5098P2=93.272kPa

Substitute 93.272kPa for P2 and 200kPa for P1 in Equation (III).

   ΔP=200kPa93.272kPa=106.728kPa

Substitute 0.23 for fL2*Dh, 3.9245 for fL1*Dh, 0.014 for f and 15cm for Dh in Equation (IV).

   L=( 3.92450.23)( 0.014 15cm× 1m 100cm )=( 3.92450.23)( 0.014 0.15m )=39.583m

Conclusion:

The duct length for velocity to be doubled is 39.583m.

The pressure drop along the length of duct is 106.728kPa.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
100 As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement: • Analytically (hand calculations) Creating Simulink Model Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and k₂ = 2 N/m. (y₁ = 0) www k₁ = 3 Jm₁ = 1 k2=2 www (Net change in spring length =32-31) (y₂ = 0) m₂ = 1 32 32 System in static equilibrium System in motion Figure Q3 - Coupled mass-spring system Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively: Analytically (hand calculations) Using MATLAB Numerical Functions (ode45) Creating Simulink Model Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If, initially, tank A contains pure water and tank B contains 20 kg of salt. A 6 L/min 0.2 kg/L x(t) 100 L 4 L/min x(0) = 0 kg 3 L/min 1 L/min B y(t) 100 L y(0) = 20 kg 2 L/min Figure Q1 - Mixing problem for interconnected tanks Determine the mass of salt in each tank at time t≥ 0: Analytically (hand calculations) Using MATLAB Numerical Functions (ode45) Creating Simulink Model Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.

Chapter 12 Solutions

Fluid Mechanics Fundamentals And Applications

Ch. 12 - Prob. 28PCh. 12 - Prob. 39PCh. 12 - Prob. 41EPCh. 12 - Prob. 64PCh. 12 - Air enters a converging—diverging nozzle with low...Ch. 12 - Prob. 75EPCh. 12 - Prob. 76EPCh. 12 - Prob. 78PCh. 12 - Prob. 79PCh. 12 - Prob. 80CPCh. 12 - On a T-s diagram of Raleigh flow, what do the...Ch. 12 - What is the effect of heat gain and heat toss on...Ch. 12 - Prob. 83CPCh. 12 - Prob. 84CPCh. 12 - Prob. 85CPCh. 12 - Argon gas enters a constant cross-sectional area...Ch. 12 - Prob. 87PCh. 12 - Prob. 88PCh. 12 - Prob. 89PCh. 12 - Prob. 90EPCh. 12 - Prob. 92EPCh. 12 - Prob. 93PCh. 12 - Prob. 94PCh. 12 - Prob. 95PCh. 12 - Prob. 96PCh. 12 - Prob. 97CPCh. 12 - Prob. 98CPCh. 12 - Prob. 99CPCh. 12 - Prob. 100CPCh. 12 - Prob. 101CPCh. 12 - Prob. 102CPCh. 12 - Prob. 103CPCh. 12 - Prob. 104CPCh. 12 - Air enters a 12-cm-diameter adiabatic duct at...Ch. 12 - Air enters a 15-m-long, 4-cm-diameter adiabatic...Ch. 12 - Air enters a 5-cm-diameter, 4-m-long adiabatic...Ch. 12 - Helium gas with k=1.667 enters a 6-in-diameter...Ch. 12 - Air enters a 15-cm-diameter adiabatic duct with...Ch. 12 - Air flows through a 6-in-diameter, 50-ft-long...Ch. 12 - Air in a room at T0=300k and P0=100kPa is drawn...Ch. 12 - Prob. 115PCh. 12 - Prob. 116PCh. 12 - Prob. 117PCh. 12 - Prob. 118PCh. 12 - Prob. 119PCh. 12 - Prob. 120PCh. 12 - Prob. 121PCh. 12 - Prob. 122PCh. 12 - A subsonic airplane is flying at a 5000-m altitude...Ch. 12 - Prob. 124PCh. 12 - Prob. 125PCh. 12 - Prob. 126PCh. 12 - Prob. 128PCh. 12 - Prob. 129PCh. 12 - Prob. 130PCh. 12 - An aircraft flies with a Mach number Ma1=0.9 at an...Ch. 12 - Prob. 132PCh. 12 - Helium expands in a nozzle from 220 psia, 740 R,...Ch. 12 - Prob. 136PCh. 12 - Prob. 137PCh. 12 - Prob. 138PCh. 12 - Prob. 139PCh. 12 - Prob. 140PCh. 12 - Prob. 141PCh. 12 - Prob. 142PCh. 12 - Prob. 143PCh. 12 - Prob. 144PCh. 12 - Prob. 145PCh. 12 - Prob. 146PCh. 12 - Prob. 147PCh. 12 - Air is cooled as it flows through a 30-cm-diameter...Ch. 12 - Prob. 149PCh. 12 - Prob. 152PCh. 12 - Prob. 155PCh. 12 - Prob. 156PCh. 12 - Prob. 157PCh. 12 - Prob. 158PCh. 12 - Prob. 159PCh. 12 - Prob. 160PCh. 12 - Prob. 161PCh. 12 - Prob. 162PCh. 12 - Prob. 163PCh. 12 - Prob. 164PCh. 12 - Assuming you have a thermometer and a device to...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License