A 16-stage axial flow compressor is to have a pressure ratio of 6.3. Tests have shown that a stage

total-to-total efficiency of 0.9 can be obtained for each of the first six stages and 0.89 for each of

the remaining 10 stages. Assuming constant work done in each stage and similar stages find the

compressor overall total-to-total efficiency. For a mass flow rate of 40 kg/s determine the power

required by the compressor. Assume an inlet total temperature of 288 K.

5. At a particular operating condition an axial flow compressor has a reaction of 0.6, a flow

coefficient of 0.5, and a stage loading, defined as ?h0/U2 of 0.35. If the flow exit angles for

each blade row may be assumed to remain unchanged when the mass flow is throttled, determine

the reaction of the stage and the stage loading when the air flow is reduced by 10% at constant

blade speed. Sketch the velocity triangles for the two conditions. Comment upon the likely

behaviour of the flow when further reductions in air mass flow are made.

6. A high-pressure axial compressor for a jet engine rotates at 15,000 rpm with an overall stagnation

pressure ratio of 8.5. The mass flow rate of air through the compressor is 16 kg/s1 and the stagnation conditions at inlet are 200 kPa and 450 K. The polytropic efficiency is 91%.

(a) If the mean radius is 0.24 m and this is constant throughout the compressor, calculate the

total-to-total isentropic efficiency of the compressor and show that, for the stage loading to

be less than 0.4 in all stages, eight stages are required.

(b) The compressor is designed with repeating stages and zero inlet swirl. If the inlet axial Mach

number is 0.52, calculate the mean flow coefficient and sketch the velocity triangles for one

stage. Show that the blade height at exit from the compressor is about 7.8 mm.

7. The preliminary design of an axial flow compressor is to be based upon a simplified consideration of the mean diameter conditions. Suppose that the stage characteristics of a repeating stage

of such a design are as follows:

Stagnation temperature rise 25C

Reaction ratio 0.6

Flow coefficient 0.5

Blade speed 275 m/s

The gas compressed is air with a specific heat at constant pressure of 1.005 kJ/(kgC). Assuming

constant axial velocity across the stage and equal absolute velocities at inlet and outlet, determine

the relative flow angles for the rotor. Physical limitations for this compressor dictate that the

space-chord ratio is unity at the mean diameter. Using Howell's correlation method, determine

a suitable camber at the midheight of the rotor blades given that the incidence angle is zero.

Use the tangent difference approximation,

tan ?

1 tan ?

2 1:55=1 1:5s=l,

for nominal conditions and the data of Figure 3.16 for finding the design deflection. (Hint: Use

several trial val

variate listributions_1/ key=9BAIPLYOBgDA MAIN MENU webwork / main311 1901/_fores s20/ 14 Divanate or Courses Homework Sets 14 bivariate 14.bivariate distributions 1: Problem 2 distributions 1 Problem 2 Previous Problem Problem List Next Problem User Settings Grades (1 point) The distributions of X and Y are described below. If X and Y are independent, determine the joint probability distribution of X and Y Problems X 0 1 POO0.21 0.79 Problem Y 1 Problem 2 P(Y) 0 47 0.22 0.31 Problem 3 Problem Note: You can eam partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining Type here to search14.bivariate distributions 1: Problem 1 ate ons Previous Problem Problem List Next Problem (1 point) igs The bivariate distribution of X and Y is described below: X Y 1 2 ms 1 0.25 0.47 2 0.1 0.18 1 A. Find the marginal probability distribution of X. n 2 n 3 m 4 2 B. Find the marginal probability distribution of Y. C. Compute the mean and variance of X. Mean = Variance = C. Compute the mean and variance of Y. Mean = Variance Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.Let X = (X. Y) be a random column vector with a bivariate normal distribution with expectation vector 0 = (0, 0) and covariance matrix I = a. Show that (Y | X = x) ~ N(ex, 1-p') and (X | Y = y) ~ N(ey, 1-p'). b. Write a Gibbs sampler to draw 10# samples from the bivariate distribution N(0, E ) and plot the data for p = 0,0.7, and 0.9