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(d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F = apª A®v° and dimensional homogeneity, find a, b and c and express F in terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F = 1 k N if the scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity u (viscosity of a fluid) is found from the formula: µAv F Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity and l is the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs µ and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.

(d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F = apª A®v° and dimensional homogeneity, find a, b and c and express F in terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F = 1 k N if the scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity u (viscosity of a fluid) is found from the formula: µAv F Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity and l is the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs µ and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter11: Heat Transfer By Radiation
Section: Chapter Questions
Problem 11.1DP
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(d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F = apª A® v° and dimensional homogeneity, find a, b and c and express F in terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F = 1 k N if the scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity µ (viscosity of a fluid) is found from the formula: µAv F F is the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity and l is the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs µ and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.
Transcribed Image Text:(d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F = apª A® v° and dimensional homogeneity, find a, b and c and express F in terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F = 1 k N if the scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity µ (viscosity of a fluid) is found from the formula: µAv F F is the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity and l is the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs µ and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.
Scenario: You are offered an apprenticeship at GE power company which has more than 125 years of integrating the latest innovations in electricity generation and its delivery including hybrid power technology. Nearly 1/3 of the electricity generated in the world uses GE equipment. GE's hybrid energy system portfolio can be customized and scaled for specific customer or system needs. Depending on the specific needs of a customer, GE can offer the following solutions for a full hybrid power generation system: • Hybrid power plant and grid feasibility studies - Determine the specific benefits a hybrid solution can provide • Hybrid power plant and equipment design – Customize the plant and equipment design to take full advantage of the hybrid components • Wind, hydro and solar forecasting via digital wind, digital hydro and digital solar farms - Evaluate the suitability of different forms of generation at a specific site • Hardware and software solutions - Combine the physical and digital to optimize performance • Turnkey construction - Provide a one-stop solution, minimizing interfaces and handoffs • Operations and maintenance - Ensure continued high performance of the assets throughout their lifecycle Part of your role as an apprentice is to spend time at GE's Power different departments and follow up the instructions of your line supervisors. Your supervisors will regularly ask you to provide technical reports and theoretical explanations about the main components and operational concepts related to these departments. [https://www.ge.com/]. In the first month, you were asked to demonstrate your engineering mathematics capabilities through dedicated tasks that should be submitted in a well written report to be reviewed by your supervisors and easily presented to sales and public relation departments. Task 1 (a) A low voltage transformer manufacturing line has a purchase order of 1700 piece. If the manufacturing line production rate is 22 piece per minute use dimensional analysis techniques to determine the time taken to produce the requested transformers to the nearest minute in hours and minutes. (b) Assume that the production time of a transformer can be given by the following formula: 1 t = Gmav-312 Where m is the mass of the transformer in kg, v is the velocity of the manufacturing line in m/s and l is the length of the production line in meters. Find the dimensions of G. (c) In b, if m = 220 grams, 1= 10.2 m, v=2.3 m/s and time is 30.1 ms. Find G?
Transcribed Image Text:Scenario: You are offered an apprenticeship at GE power company which has more than 125 years of integrating the latest innovations in electricity generation and its delivery including hybrid power technology. Nearly 1/3 of the electricity generated in the world uses GE equipment. GE's hybrid energy system portfolio can be customized and scaled for specific customer or system needs. Depending on the specific needs of a customer, GE can offer the following solutions for a full hybrid power generation system: • Hybrid power plant and grid feasibility studies - Determine the specific benefits a hybrid solution can provide • Hybrid power plant and equipment design – Customize the plant and equipment design to take full advantage of the hybrid components • Wind, hydro and solar forecasting via digital wind, digital hydro and digital solar farms - Evaluate the suitability of different forms of generation at a specific site • Hardware and software solutions - Combine the physical and digital to optimize performance • Turnkey construction - Provide a one-stop solution, minimizing interfaces and handoffs • Operations and maintenance - Ensure continued high performance of the assets throughout their lifecycle Part of your role as an apprentice is to spend time at GE's Power different departments and follow up the instructions of your line supervisors. Your supervisors will regularly ask you to provide technical reports and theoretical explanations about the main components and operational concepts related to these departments. [https://www.ge.com/]. In the first month, you were asked to demonstrate your engineering mathematics capabilities through dedicated tasks that should be submitted in a well written report to be reviewed by your supervisors and easily presented to sales and public relation departments. Task 1 (a) A low voltage transformer manufacturing line has a purchase order of 1700 piece. If the manufacturing line production rate is 22 piece per minute use dimensional analysis techniques to determine the time taken to produce the requested transformers to the nearest minute in hours and minutes. (b) Assume that the production time of a transformer can be given by the following formula: 1 t = Gmav-312 Where m is the mass of the transformer in kg, v is the velocity of the manufacturing line in m/s and l is the length of the production line in meters. Find the dimensions of G. (c) In b, if m = 220 grams, 1= 10.2 m, v=2.3 m/s and time is 30.1 ms. Find G?
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