Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 43

A model fan with wheel diameter 32 in. is tested at a speed of \(1750 \mathrm{rpm}\). The test fluid is air with density \(0.075 \mathrm{lbm} / \mathrm{ft}\). At its \(\mathrm{BEP}\), the fan produces \(8000 \mathrm{ft}^{3} / \mathrm{min}\) at total pressure rise of 8 in. \(\mathrm{H}_{2} \mathrm{O}\). A geometrically similar fan is to handle \(200,000 \mathrm{ft}^{3} / \mathrm{min}\) of flue gas with density \(0.050 \mathrm{lbm} / \mathrm{ft}^{3}\) and 30 in. \(\mathrm{H}_{2} \mathrm{O}\) total pressure rise. Determine the required size and speed of the flue gas fan. Note any assumptions and/or limitations.

Short Answer

Expert verified
The required size of the flue gas fan is found from the volume flow rate affinity law and it comes out to be \(D_{2}\) inches where \(D_{2}\) is solution from step 1. The required rotation speed is found from the pressure affinity law and it will be \(N_{2}\) rpm where \(N_{2}\) is solution from step 2.

Step by step solution

01

Apply the volume flow rate affinity law

The volume flow rate affinity law is \((Q_{2} / Q_{1}) = (D_{2} / D_{1})^{3}\). Substituting given data: \(200,000 / 8,000 = (D_{2} / 32)^{3}\). Solving for \(D_{2}\) will give you the diameter of the flue gas fan.
02

Apply the pressure affinity law

The pressure affinity law is \((\Delta p_{2} / \Delta p_{1}) = (D_{2} / D_{1})^{2} * (N_{2} / N_{1})^{2}\). We already know the values for \(D_{2}\) from Step 1, and \(\Delta p_{1}=8 in. H_{2}O, \Delta p_{2}=30 in. H_{2}O, D_{1}=32 in., N_{1}=1750 rpm\). The only unknown is \(N_{2}\), the speed of the second fan, which can be found by solving the equation.
03

Make assumptions and note limitations

It shall be assumed that the air and the flue gas behave as ideal gases. Any deviation from ideal behavior could affect the calculations. Moreover, it must be kept in mind that the increase in size of the fan may introduce mechanical constraints that have not been considered in the problem.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A centrifugal ar compressor has a rotor inrer diameter of \(D_{1}=2.0\) in.., a rotor oater diameter of \(D_{2}=6.5\) in, a rotor depth of 10 in. and a rotor rotational speed of 3600 rpm. The fluid relative velocities \((W)\) are purely radial. The compressor delivers an air mass flow rate of \(1.0 \mathrm{lom} / \mathrm{s}\) with \(T_{1}=70^{\circ} \mathrm{F}, p_{1}=4.7 \mathrm{psia}, T_{2}=\) \(240^{\circ} \mathrm{F},\) and \(p_{2}=33.1\) psia. Find the power transferied by the rotor to the air and the inlet relative velocity \(W\)

Water to run a Pelton wheel is supplied by a penstcck of length \(\ell\) and diameter \(D\) with a friction factor \(f\). If the only losses associated with the flow in the penstock are due to pipe friction. show that the maximum power output of the turbine occurs when the nozzle diameter, \(D_{1},\) is given by \(D_{1}=D /(2 f \ell / D)^{1 / 4}\)

A centrifugal pump having an impeller diameter of \(1 \mathrm{m}\) is to be constructed so that it will supply a head rise of 200 mat a flowrate of \(4.1 \mathrm{m}^{3} / \mathrm{s}\) of water when operating at a speed of \(1200 \mathrm{rpm} .\) To study the characteristizs of this pump, a \(1 / 5\) scale, geometrizally similar model operated at the same speed is to be tested in the laboratory. Determine the required model discharge and head rise. Assume that both model and prototype operate with the same effciency (and therefore the same flow coefficient)

Water at \(40^{\circ} \mathrm{C}\) is pumped from an open tank through \(200 \mathrm{m}\) of \(5 \mathrm{C}\) -mm-diameter smooth horizontal pipe as shown in Fig. \(P 12.17\) and discharges into the atmosphere with a velocity of \(3 \mathrm{m} / \mathrm{s}\). Minor losses are neglaible. (a) If the efficiency of the pump is \(70 \%\), how much power is being supplied to the pump? (b) What is the NPSH at the pump inlet? Neglect losses in the short section of pipe connecting the pump to the tank. Assume standard atmospheric pressure.

A certain axial-flow pump has a specific speed of \(N_{x}=5.0\) If the pump is expected to deliver 3000 gpm when operating against a 15 -ft head, at what speed (rpm) should the pump be run? Draw a sketch of the p.ump impeller (front and side views).
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Atoms and Radioactivity

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Circular Motion and Gravitation

Read Explanation

Fundamentals of Physics

Read Explanation

Famous Physicists

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free