Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 11, Problem 11.102P
To determine

The rate of water flow should be determined in gal/min for given multiblade HAWT.

Expert Solution & Answer
Check Mark

Answer to Problem 11.102P

The water flow rate in the multiblade HAWT is 29.44 gal.min.

Explanation of Solution

Given Information:

Wind speed, 12 min/h

Diameter of cast iron pipe = 3 in.

Height, 10 ft

Diameter of turbine, 6 ft

First let us find out the speed of wind for the given system,

V=12 min/hV= 12minh×5280 ft1min×1h3600sV=17.6 ft/s

For the given turbine, the area would be,

A=πD24A=π×( 6)24A=28.27 ft2

From this, we can determine the maximum power delivered by turbine.

Pmax=Cpρ2AV3

Where,

Cp

  • = maximum value of power coefficient
  • ρ
  • = air density
  • V = wind speed of given system

In above equation, putting the values for V, A, Cp and p.

Pmax=Cpρ2AV3Pmax=0.29×0.00232×28.27×(17.6)3Pmax=51.41 ftlbf/s

Let us consider, that the pump efficiency is η=0.8, which give the pump power as:

Ppump=η×51.41 ftlbf/sPpump=0.8×51.41 ftlbf/sPpump=41.13 ftlbf/s

The relation of the pump power with system is as below:

Ppump=ρwatergQHsystem...(1)

For above equation, we have density of water, ρwater=1.94 slug/ft3.

The head of system has a formula of;

Hsystem=Δz+fLdVpipe22g...(2)

Where:

Δz

  • = height
  • f = friction factor
  • Vpipe = pipe velocity
  • d = diameter of the pipe

For getting the head of system, we need to find out velocity of pipe, Vpipe.

Vpipe=4QπD2Vpipe=4Qπ×( 0.25)2Vpipe=20.37Q

In equation (2), putting the values,

Hsystem=Δz+fLdVpipe22gHsystem=10+f100.25×( 20.37×Q)22×32.2Hsystem=10+258fQ2

Putting the values from above in equation (1),

Ppump=ρwatergQHsystem41.13=1.94×32.2Q(10+258fQ2)Q(10+258fQ2)=0.658...(3)

The dynamic viscosity of water and for cast iron pipe, we have μ=2.09×105slug/fts and ε=0.00085 m.

Now determining the Reynolds number and the ratio for the system as:

Re=ρVpipedμRe=1.94×20.37×Q×0.25×1052.09Re=472701Q;andεd=0.000850.25=0.0034

For the given system, applying the Moody’s equation,:

1f=2log[εD3.7+2.51 Redf]1f=2log[0.00343.7+2.51472701Qf]1f=2log[0.00092+0.0000053Qf]...(4)

By solving the equations (3) & (4).

We get f=0.0306 and Q =0.0656 ft3/s.

Converting the flow rate into gal/min.

Q=0.0656 ft3/sQ=0.0656 ft3s×7.48052 gal1 ft3×60 sminQ=29.44 gal/min

So, the water flow rate in the multiblade HAWT is 29.44 gal.min.

Conclusion:

The water flow rate in the multiblade HAWT is 29.44 gal.min.

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 11 Solutions

Fluid Mechanics

Ch. 11 - Prob. 11.11PCh. 11 - Prob. 11.12PCh. 11 - Pl 1.13 A 3.5 hp pump delivers 1140 lbf of...Ch. 11 - Prob. 11.14PCh. 11 - Prob. 11.15PCh. 11 - Prob. 11.16PCh. 11 - Prob. 11.17PCh. 11 - Prob. 11.18PCh. 11 - Pl 1.19 A centrifugal pump has r2 = 9 in, b2 = 2...Ch. 11 - Prob. 11.20PCh. 11 - Prob. 11.21PCh. 11 - Prob. 11.22PCh. 11 - P11.23 When pumping water, (a) at what speed...Ch. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Tests by the Byron Jackson Co. of a...Ch. 11 - A pump, geometrically similar to the 12.95-in...Ch. 11 - Prob. 11.31PCh. 11 - Prob. 11.32PCh. 11 - Prob. 11.33PCh. 11 - You are asked to consider a pump geometrically...Ch. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37PCh. 11 - Prob. 11.38PCh. 11 - Prob. 11.39PCh. 11 - Prob. 11.40PCh. 11 - Prob. 11.41PCh. 11 - Prob. 11.42PCh. 11 - The 28-in-diameter pump in Fig. 11.7a at 1170...Ch. 11 - Prob. 11.44PCh. 11 - Prob. 11.45PCh. 11 - Prob. 11.46PCh. 11 - PI 1.47 A pump must be designed to deliver 6 m /s...Ch. 11 - Pl 1.48 Using the data for the pump in Prob. Pl...Ch. 11 - Prob. 11.49PCh. 11 - Prob. 11.50PCh. 11 - Prob. 11.51PCh. 11 - Prob. 11.52PCh. 11 - Prob. 11.53PCh. 11 - Prob. 11.54PCh. 11 - Prob. 11.55PCh. 11 - Prob. 11.56PCh. 11 - Prob. 11.57PCh. 11 - Prob. 11.58PCh. 11 - Suppose it is desired to deliver 700 ftVmin of...Ch. 11 - Prob. 11.60PCh. 11 - Prob. 11.61PCh. 11 - Prob. 11.62PCh. 11 - Pl 1.63 A good curve-fit to the head vs. flow for...Ch. 11 - Prob. 11.64PCh. 11 - *P11.65 An 11.5-in-diameter centrifugal pump,...Ch. 11 - Pl 1.66 It is proposed to run the pump of Prob. Pl...Ch. 11 - Prob. 11.67PCh. 11 - Prob. 11.68PCh. 11 - The pump of Prob. P1138, running at 3500 r/min, is...Ch. 11 - Prob. 11.70PCh. 11 - Prob. 11.71PCh. 11 - Prob. 11.72PCh. 11 - Prob. 11.73PCh. 11 - Prob. 11.74PCh. 11 - Prob. 11.75PCh. 11 - Prob. 11.76PCh. 11 - Prob. 11.77PCh. 11 - Prob. 11.78PCh. 11 - Prob. 11.79PCh. 11 - Determine if either (a) the smallest or (b) the...Ch. 11 - Prob. 11.81PCh. 11 - Prob. 11.82PCh. 11 - Prob. 11.83PCh. 11 - Prob. 11.84PCh. 11 - Prob. 11.85PCh. 11 - Prob. 11.86PCh. 11 - Prob. 11.87PCh. 11 - Prob. 11.88PCh. 11 - A Pelton wheel of 12-ft pitch diameter operates...Ch. 11 - Prob. 11.90PCh. 11 - Prob. 11.91PCh. 11 - Prob. 11.92PCh. 11 - Prob. 11.93PCh. 11 - Prob. 11.94PCh. 11 - Prob. 11.95PCh. 11 - Prob. 11.96PCh. 11 - Prob. 11.97PCh. 11 - Prob. 11.98PCh. 11 - Prob. 11.99PCh. 11 - Prob. 11.100PCh. 11 - Prob. 11.101PCh. 11 - Prob. 11.102PCh. 11 - Prob. 11.103PCh. 11 - Prob. 11.104PCh. 11 - Prob. 11.105PCh. 11 - Prob. 11.106PCh. 11 - Prob. 11.107PCh. 11 - Prob. 11.108PCh. 11 - Prob. 11.1WPCh. 11 - Prob. 11.2WPCh. 11 - Prob. 11.3WPCh. 11 - Prob. 11.4WPCh. 11 - Prob. 11.5WPCh. 11 - Consider a dimensionless pump performance chart...Ch. 11 - Prob. 11.7WPCh. 11 - Prob. 11.8WPCh. 11 - Prob. 11.9WPCh. 11 - Prob. 11.10WPCh. 11 - Prob. 11.1CPCh. 11 - Prob. 11.2CPCh. 11 - Prob. 11.3CPCh. 11 - Prob. 11.4CPCh. 11 - Prob. 11.5CPCh. 11 - Prob. 11.6CPCh. 11 - Prob. 11.7CPCh. 11 - Prob. 11.8CPCh. 11 - Prob. 11.1DP
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
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License