Engineering High School

A water turbine is to be designed to produce 27MW when running at 93.7 rev/min
under a head of 16.5m. A model turbine with an output of 37.5kW is tested under
dynamically similar conditions with a head of 4.9m . Calculate the:
a. model speed; b. scale ratio; c. assuming a model efficiency of 88%, estimate the volume
flow rate through the model; and d. if it is estimated that the force on the thrust bearing of
the full-size machine is 7.0GN , determine the bearing thrust of the model.

Answers

Answer 1

The Answers for the given question are as follow:

a. The model speed is approximately 31.62 rev/min.

b. The scale ratio is approximately 0.0417.

c. The estimated volume flow rate through the model is approximately 943.44 m^3/s.

d. The bearing thrust of the model is approximately 9.72 kN.

To calculate the required values for the water turbine model, we can utilize the concept of dynamic similarity.

a. To find the model speed, we can use the principle of geometric similarity, which states that the ratio of speeds is equal to the ratio of the square roots of the head. Thus:

Model speed = (√(Model head))/(√(Full-size head)) * Full-size speed

= (√4.9/√16.5) * 93.7 rev/min

= 31.62 rev/min

b. The scale ratio can be determined using the equation:

Scale ratio = (√(Model power))/(√(Full-size power))

= (√37.5kW)/(√27MW)

≈ 0.0417

c. To estimate the volume flow rate through the model, we can use the power equation:

Model power = (Model efficiency) * (Volume flow rate) * (Model head) * (Gravity)

37.5kW = 0.88 * (Volume flow rate) * 4.9m * (9.81m/s^2)

Solving for the volume flow rate:

Volume flow rate = 37.5kW / (0.88 * 4.9m * 9.81m/s^2)

≈ 943.44 m^3/s

d. To calculate the bearing thrust of the model, we can use the principle of force similarity:

Bearing thrust model = (Model power / Full-size power) * Full-size bearing thrust

= (37.5kW / 27MW) * 7.0GN

≈ 9.72kN

For more questions on force, click on:

https://brainly.com/question/12785175

#SPJ8

Related Questions

Other Questions

Edwin sells jars of jam for $1.90 each. Determine how many jars of jam Edwin needs to sell to break even if the variable cost per jar is $1.10 and fixed expenses are $35,700.00 per year. We also see that the manufacturing firms in this province increased the number of informal workers they used from third-party contractors from 10,000 to 14,000 workers after the implementation of the new minimum wage law. What is the cross- wage elasticity of demand? Are formal and informal workers substitutes or complements in manufacturing? Evaluate the motivational considerations that should be made in the setting up of a budgetary planning and control system especially during the COVID-19pandemic. select the correct answer. which religion was popular in india before the development of hinduism during the gupta reign? a.buddhism b.christianity c.islam d.daoism How the laddering technique of interviewing helps the marketers to probe cognitive structures of individuals related to some brand or product they use. Why this information is important for the marketer. Take a product (or brand) that you consume and try to identify the attributes, consequences and value that you gain by using that product/brand. The single most important component of an annual report is the:A.balance sheet.B.income statement.C.cash flow statement.D.signature of a Certified Public Accountant.E.signature of the firm's owners or stakeholders. D Question 3 1 pts The price of electric cars goes down. Illustrate the impact on supply, demand, and equilibrium price and quantity in the market for gas powered cars, assuming they are substitutes. You purchased one share of microsoft corp. one year ago for $141.00 per share. The company paid a dividend of $.51 per share during the year and had an ending share price of $150.50. What is the percentage return on your investment?.36%6.74%7.10%8.80%9.45% Merger NPV Harrods PLC has a market value of 310 million and 11 million shares outstanding. Selfridge Department Store has a market value of 121 million and 6 million shares outstanding. Harrods is contemplating acquiring Selfridge. Harrodss CFO concludes that the combined firm with synergy will be worth 475 million, and Selfridge can be acquired at a premium of 13 million.a. If Harrods offers 8.5 million shares of its stock in exchange for the 6 million shares of Selfridge, what will the stock price of Harrods be after the acquisition?b. What exchange ratio between the two stocks would make the value of the stock offer equivalent to a cash offer of 134 million? by convention a cache is named by the amount of data it holds. for example a 4kib cache hold 4kib of data. however, you need additional bits per line to hold the metadata such as the tag and the valid bit. for this exercise, you will examine how the configuration of the cache affects the total number of bits needed to implement the cache. for all parts of this question, assume that the cache is byte addressable and that the address is 64 bits and assume that each word is also 64 bits. hint: you need to compute the number of bits needed for the is over 100,000. while the cache size is labeled in terms of data stored, like 4kib cache is 4kib of data, you still need the other bits to complete the implementation! 3.1 calculate the total number of bits required for to implement a direct-mapped 32kib cache with two-word blocks. 3.2 calculate the total number of bits required for to implement a direct-mapped 64kib cache with 16-word blocks. how does the total number of bit compare with the 32kib cache in q3.1 3.3 explain why a 64kib cache, despite being larger, might provide slower performance than the first cache. assume the hit time and miss penalties are identical. 3.4 generate a series of read requests that have a lower miss rate on a 32kib two-way set associative cache then on the cache described in 3.1. According to Maslow's Hierarchy of Needs, a company is addressing the need for __________ when it organizes a yearly picnic (l) for employees and their families. A scientist pours 1 liter of pure water into the ocean at a site near Greenland.(a) How long (approximately) might be required for this water to become uniformly distributed over the entire global ocean, from the ocean surface to the seafloor? Would this be the same as the residence time? Explain in a few sentences.(b) After the water has become uniformly distributed, another scientist collects 1 liter of water from the ocean at a point near Hawaii. How many molecules of water from the original liter (Greenland) would be present in the liter of water collected near Hawaii? [Useful fact: the volume of the world ocean is about 1.3109 km3]Please answer both of the questions A non-numerical cost estimation technique whereby managerial judgement is employed to determine wheth- a cost is fixed, variable or mixed is known as: Select one: a. The Graphical Method. b. The High-Low Method. c. Account Analysis. d. The Least-Squares-Regression Method. Describe the similarities and differences in solving the equations 4x + 1 = 3 and 4sin theta + 1 = 3 Exercise 3: Let {Bt, t 0} be a standard Brownian motion. Let 0 < s < t and a, b E R. (a) Calculate E (aBs + bBt). (b) Show that Var (aBs + bBt) = (a + b)s + b(t-s). (c) What is the distribution Fresh off the excitement of the 2012 London Olympic Games, you decide that you want your firm to take advantage of the profits to be made for the 2016 games in Rio de Jeneiro. To do so you plan to open a factory in Brazil. After examining the idea, your CFO projects revenues next year (2013) to be $16 million and costs to be $7 million. Both of these are expected to grow at a rate of 22.0% per year as the excitement for the games builds. Your firm faces a 21% tax rate, a 13.5% discount rate and you can depreciate your new investment using the straight line method over the four years leading up to the games, at which point the value of the venture moving forward will be $7 million. This $7 million is the after-tax terminal value that is in year 4 (that is, 2016) dollars and is the PV of all cash flows year 5 and beyond. The capital expenditure of this project is $12 million. What is the NPV of the project? Assume that you have no significant working capital costs. The statistician for an ice cream shop has produced a best fit line for the relationship between average daily sales in 1000s of dollars, y, and the high temperature for the day in Celsius, X. The equation for the line is y = 4.1 +0.12.x. If the high temperature for a particular day was 31C, and the residual for the sales was $300, what were the actual sales that day? Suppose you deposit $50 each week into anaccount earning 3% interest for 8 years. How much will you have atthe end? Round to the nearest dollar. In the True or False questions below, give a simple justification. If true, justify by an argument/theorem; If False, give a counter-example; do not correct the statement.1. The vectors (1+i, i) and (i, 1-i) in C are orthogonal. 2. There is a normal matrix which is not Hermitian. 3. If two nonzero vectors in an IPS are orthogonal, then they are linearly independent. 4. In an IPS, if (x, y) = 0 for all x, then y = 0. 5. Every nonzero finite dimensional IPS has an orthonormal basis. when working with charts the green cross that appears next to a chart when editing when working with charts the green cross that appears next to a chart when editing allows the user to add data labels. allows the user to add axis titles but not data labels. allows the user to change chart styles. allows the user to filter series.