Question
(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
(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?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started