(a) Prove that the centrifugal stress at the root of an untapered blade attached to the drum of an

axial flow turbomachine is given by

?c ??mN2

Ax=1800,

where ?m density of blade material, N rotational speed of drum, in rpm and Ax area of

the flow annulus.

(b) The preliminary design of an axial-flow gas turbine stage with stagnation conditions at stage

entry of p01 400 kPa, T01 850 K, is to be based upon the following data applicable to the

mean radius:

Flow angle at nozzle exit, ?2 63.8;

Reaction, R 0.5;

Flow coefficient, cx/Um 0.6;

Static pressure at stage exit, p3 200 kPa;

Estimated total-to-static efficiency, ?ts 0.85.

Assuming that the axial velocity is unchanged across the stage, determine

(i) the specific work done by the gas;

(ii) the blade speed;

(iii) the static temperature at stage exit.

(c) The blade material has a density of 7850 kg/m3 and the maximum allowable stress in the

rotor blade is 120 MPa. Taking into account only the centrifugal stress, assuming untapered

blades and constant axial velocity at all radii, determine for a mean flow rate of 15 kg/s

(i) the rotor speed (rev/min);

(ii) the mean diameter;

(iii) the hub-tip radius ratio.

For the gas assume that CP 1050 J/(kg K) and R 287 J/(kg K)

Consider a motor vehicle department that operates as follows. Each customer sees a clerk (receptionist) to check their documents for accuracy. The service time per customer (in minutes) can take any value between 2 to 5 minutes. Then, each customer require service on (a) getting or renewing a driver's license or registering an automobile, or leave. 30% of customers get or renew a driver's license, 50% of the customers register an automobile and the remaining 20% of customers leave the service. The service time for getting or renewing a driver's license is gamma distributed with shape parameter 3 and scale parameter 10. Registering a car is a new service offered to customers in this department so the management lacks data to find the best distribution to represent the characteristics of this service. However, the experts believe that the service time is usually between 10 to 35 minutes with 20% chance of being less than 15 minutes, 60% chance of being less than 25 minutes and 95% chance of being less than 30 minutes. Labor costs are $20 per hour for the receptionist, $30 for the clerk who serve people getting or renewing their driver's license, $40 for the clerk who helps customer to register an automobile. Develop a simulation model for this system and answer the following questions:

a.What is the mean and standard deviation of the service time per customer (do not include waiting time)?

b.What is the probability that the service time per customer will be less than 8 minutes? What is the probability that the service time per customer will exceed 20 minutes?

c.What is the mean and standard deviation of the labor cost per customer to deliver this service?

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? 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)A high-production operation manufactures a part for the automotive indus- try. Starting material cost = $1.75, and cycle time = 2.20 min. Equipment cost rate = $42.00/hr, and labor cost rate = $24.00/hr, including overhead costs in both cases, Availability of the production machine in this job = 97%, and the scrap rate of 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 0, what would be the production rate and finished part cost?Find E. Replace Picture Paint Date and Insert drawing time object Select all Paragraph Insert Editing 5 Suppose a delay in starting production due to an expected mechanical failure is anywhere from 0 to 30 minutes. Assuming that X is uniform random variable, find: A) The probability that production will be delayed by less than 10 minutes B) The probability that production will be delayed by more than 20 minutes C) The probability that production will be delayed by 12 to 20 minutes