Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 63

It is desired to produce 50,000 hp with a head of \(50 \mathrm{ft}\) and an angular velocity of \(100 \mathrm{rpm} .\) How many turbines would be needed if the specific speed is to be (a) 50 (b) \(100 ?\)

Short Answer

Expert verified
For specific speed 50, the number of turbines needed is calculated to be 0.32, and for specific speed 100, the number of turbines needed is calculated to be 0.08. In both cases, the number of turbines must be rounded up to the nearest whole number because it is not possible to operate a fraction of a turbine. Therefore, for specific speed 50, 1 turbine is needed and for specific speed 100, also 1 turbine is needed.

Step by step solution

01

Calculate number of turbines for specific speed 50

First, plug in the values into the formula for the number of turbines. Let us assume that power is \(P = 50,000hp\), head \(H = 50 ft\), and specific speed \(n_s = 50\). So, \(N_t = \frac{50000}{50^2 * 50^{5/2}}\)
02

Calculate number of turbines for specific speed 100

Now, calculate the number of turbines for the specific speed 100. Plug in the values into the formula for the number of turbines where \(P = 50,000hp\), \(H = 50ft\) and \(n_s = 100\). Hence, \(N_t = \frac{50000}{100^2 * 50^{5/2}}\)

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

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)

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.

The system resistance for a pipeline is given by \(\Delta p_{\mathrm{sys}}=2.0 Q^{2}\) where \(\Delta p_{\text {ys }}\) is the pressure rise required of a pump to deliver the flow rate \(Q\) through the piping system. A pump has the pressure-rise-flow characteristic given by \(\Delta p_{p}=30.0-3.0 Q^{2} .\) In both curves, \(\Delta p\) is in \(\mathrm{kPa}\) and \(Q\) is in \(\mathrm{m}^{3} / \mathrm{s}\), Find the pump input power if this punp is placed in this piping system and the pump overall eff ciency is \(90 \%\)

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 \(W\)
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Electricity

Read Explanation

Atoms and Radioactivity

Read Explanation

Torque and Rotational Motion

Read Explanation

Waves Physics

Read Explanation

Thermodynamics

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