Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 13, Problem 26P
To determine

The force required to move the plate toward the water jet.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

The elbow angle is (θ) is 110°.

The cross sectional area at inlet (A1) is 150cm2.

The cross sectional area at exit (A2) is 25cm2.

The elevation difference (z2z1) is 40cm.

The mass flow rate (m˙) is 30kg/s.

The mass of the elbow with water (m) is 50kg.

The momentum flux correction factor β is 1.03.

Calculation:

Calculate the weight density of water by using the relation.

    W=mg=(50kg)(9.81m/s2)=490.5kgm/s2(1N1kgm/s2)=490.5N

Calculate the velocity at the inlet (V1) of the pipe using the relation.

  V1=m˙ρA1=30kg/s(1000kg/m3)(150cm2(1m100cm)2)=2.0m/s

Calculate the velocity at the outlet (V2) of the pipe using the relation.

  V2=m˙ρA2=30kg/s(1000kg/m3)(25cm2(1m100cm)2)=12.0m/s

Calculate the gauge pressure at the center on the inlet of the elbow by using Bernoulli’s

Equation.

    p1ρg+V122g+z1=p2ρg+V222g+z2p1p2=ρg(z2z1+V22V122g)

  p=ρg(z2z1+V22V122g)=[(1000(Kg/m3))(9.81(m/s2))(40cm(1m100cm)+((12m/s)2(2m/s)22(9.81m/s)))×(1kN1000kg.m/s2)]=73.9kN/m2(1kPa1kN/m2)=73.9kPa

Calculate the anchoring force in x direction by using moment equation.

  Frx+p1A1=βm˙V2cosθβm˙V1Frx=βm˙(V2cosθV1)p1A1=[1.03(30kg/s)(12cos110°2)m/s(1kN1000kg.m/s2)(73.9kN/m2)((150cm)(1m100cm))2]=1.297kN

Calculate the anchoring force in y direction by using moment equation.

    Frz=βm˙V2sinθ+W=1.03(30kg/s)(12sin110°m/s)(1kN1000kg.m/s2)+0.4905kN=0.8389kN

Calculate the total anchoring force by using the expression.

    Fr=Frx2+Fry2=(1.297kN)2+(0.8389kN)2=1.54kN

Calculate the angle of the total anchoring force by using the expression.

    θ=tan1(FrzFrx)=tan1(0.83891.297)=32.9°

Thus, the anchoring force needed to hold the elbow is 1.54kN_ in the direction of negative in the direction of 32.9°.

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!

Chapter 13 Solutions

Fundamentals of Thermal-Fluid Sciences

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.
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
Fluid Mechanics - Viscosity and Shear Strain Rate in 9 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=_0aaRDAdPTY;License: Standard youtube license