Derive an approximate expression for the total-to-total efficiency of a turbine stage in terms of

the enthalpy loss coefficients for the stator and rotor when the absolute velocities at inlet and

outlet are not equal. A steam turbine stage of high hub-tip ratio is to receive steam at a stagnation

pressure and temperature of 1.5 MPa and 325C, respectively. It is designed for a blade speed of

200 m/s and the following blade geometry was selected:

Nozzles Rotor

Inlet angle, degree 0 48

Outlet angle, degree 70.0 56.25

Space-chord ratio, s/l 0.42 ?

Blade length-axial chord ratio, H/b 2.0 2.1

Maximum. thickness-axial chord 0.2 0.2

The deviation angle of the flow from the rotor row is known to be 3 on the evidence of cascade

tests at the design condition. In the absence of cascade data for the nozzle row, the designer

estimated the deviation angle from the approximation 0.19 ?s/l where ? is the blade camber

in degrees. Assuming the incidence onto the nozzles is zero, the incidence onto the rotor

1.04, and the axial velocity across the stage is constant, determine

(i) the axial velocity;

(ii) the stage reaction and loading factor;

(iii) the approximate total-to-total stage efficiency on the basis of Soderberg's loss correlation,

assuming Reynolds number effects can be ignored;

(iv) by means of a large steam chart (Mollier diagram) the stagnation temperature and pressure at

stage exit.

9. (a) A single-stage axial flow turbine is to be designed for zero reaction without any absolute

swirl at rotor exit. At the nozzle inlet the stagnation pressure and temperature of the gas

are 424 kPa and 1100 K, respectively. The static pressure at the mean radius between the

nozzle row and rotor entry is 217 kPa and the nozzle exit flow angle is 70. Sketch an appropriate Mollier diagram (or a Ts diagram) for this stage allowing for the effects of losses and

sketch the corresponding velocity diagram. Hence, using Soderberg's correlation to calculate

blade row losses, determine for the mean radius

2} A machine center with 5 stations has two categories of downtime: machine jams from defective components and electromechanical failures. All 5 stations have a fraction defect rate of .1125 with a probability of a jam being .25. Each jam takes 2 minutes to x before the machine can run again. For electromechanical failures, the machine center has a failure rate of 0.05 and downtime for these issues require an average of 5 minutes to fix the problem. The ideal cycle time is 30 seconds. a. What is the hourly production rate? b. What is proportion of acceptable product? c. What is the line efciency? 1. (25 pts.) The class registrations of 50 mechanical engineering students are analyzed. It is found that: *5 students take all three subjects (Dynamics, Statistics, and Fluid Mechanics), Dynamics * 18 students take Dynamics and Statistics, * 9 students take Dynamics and Fluid Mechanics, *7 students take Statistics and Fluid Mechanics, * 29 students take Dynamics, * 15 students take Fluid Mechanics, * 1 student takes none of the three. Statistics Fluid (1) How many students take only Statistics? (2) What is the probability that a student selected at random takes all three, given she/he takes Statistics? (3) If one of the students who take at least two of the three courses is chosen at random, what is the probability that he or she takes all three courses? (4) n(Statistics ( Dynamics) = ? (5) n Statistics ~ Fluid Dynamics) = ?18. Goshawks Co. produces an automotive product and incurs total manufacturing costs of $2,600,000 in the production of 80,000 units. The company desires to earn a profit equal to a 10% rate of return on assets of $960,000. Total selling and administrative expenses are $105,000. Calculate the markup percentage, using the total cost concept. (4 pts) Compute the price of the automotive product. (4 pts)Example 1.4 A high-production operation manufacturers a part for the automotive industry. Starting material cost = $2.15, and cycle time = 2.35 min. Equipment cost rate = $40.00/hr, and labor cost rate = $22.00/hr, including overhead costs in both cases. Availability of the production machine in this job = 97% and the scrap rate of the parts produced 5%. Because this is a long-running job, setup time is ignored, and there is no tooling cost to be considered. (a) Determine the production rate and finished part cost in this operation. (b) If availability could be increased to 100% and scrap rate could be reduced to zero, what would be the production rate and finished part cost