Solve the following

Q.1 The eye of a centrifugal compressor has a hub-tip radius ratio of 0.4, a maximum relative flow

Mach number of 0.9, and an absolute flow that is uniform and completely axial. Determine the

optimum speed of rotation for the condition of maximum mass flow given that the mass flow rate

is 4.536 kg/s. Also, determine the outside diameter of the eye and the ratio of axial velocity-

blade speed at the eye tip. Figure 7.11 may be used to assist the calculations.

5. An experimental centrifugal compressor is fitted with free-vortex guide vanes to reduce the relative air speed at inlet to the impeller. At the outer radius of the eye, air leaving the guide vanes

has a velocity of 91.5 m/s at 20 to the axial direction. Determine the inlet relative Mach number,

assuming frictionless flow through the guide vanes, and the impeller total-to-total efficiency.

Other details of the compressor and its operating conditions are

Impeller entry tip diameter, 0.457 m;

Impeller exit tip diameter, 0.762 m;

Slip factor, 0.9 Radial blades at impeller exit;

Radial component of velocity at impeller exit, 53.4 m/s;

Rotational speed of impeller, 11,000 rev/min;

Static pressure at impeller exit, 223 kPa (abs).

6. A centrifugal compressor has an impeller with 21 vanes, which are radial at exit, a vaneless diffuser, and no inlet guide vanes. At inlet the stagnation pressure is 100 kPa (abs) and the stagnation temperature is 300 K.

(i) Given that the mass flow rate is 2.3 kg/s, the impeller tip speed is 500 m/s and the mechanical

efficiency is 96%, determine the driving power on the shaft. Use eqn. (7.34b) for the slip factor.

(ii) Determine the total and static pressures at diffuser exit when the velocity at that position is

100 m/s. The total-to-total efficiency is 82%.

(iii) The reaction, which may be defined as for an axial flow compressor by eqn. (5.19), is 0.5,

the absolute flow speed at impeller entry is 150 m/s, and the diffuser efficiency is 84%.

Determine the total and static pressures, absolute Mach number, and radial component

of velocity at the impeller exit.

(iv) Determine the total-to-total efficiency for the impeller.

(v) Estimate the inlet-outlet radius ratio for the diffuser assuming the conservation of angular

momentum.

(vi) Find a suitable rotational speed for the impeller given an impeller tip width of 6 mm.

7. A centrifugal pump is used to raise water against a static head of 18.0 m. The suction and

delivery pipes, both 0.15 m diameter, have, respectively, friction head losses amounting to 2.25

and 7.5 times the dynamic head. The impeller, which rotates at 1450 rev/min, is 0.25 m diameter

with eight vanes, radius ratio 0.45, inclined backwards at ?

0

2 60. The axial width of the impeller

is designed so as to give constant radial velocity at all radii and is 20 mm at impeller exit. Assuming

a hydraulic efficiency of 0.82 and an overall efficiency of 0.72, determine

(i) the volume flow rate;

(ii) the slip factor using Busemann's method;

(iii) the impeller vane inlet angle required for zero incidence angle;

(iv) the power required to drive the pump.

2. Suppose 42%% of Ph.D.s in statistics/biostatistics are earned by women and a random sample 36 statistics/biostatistics Ph.Dis is obtained. (You may want to use technology to compute some of the probabilities.) a. What's the probability none of the 36 statistics/biostatistics Ph.D.s are women? b. What's the probability at least 1 of the 36 statistics/biostatistics Ph.D.s is a woman? c. How many women do you expect in the sample of the 35 statistics/biostatistics Ph.D.s? d. What's the probability fewer than half of the 36 statistics/biostatistics Ph.D.s are women?k. Suppose the sample actually consists of 14 women and 22 men and a subset of 6 is chosen for a panel discussion. i. What's the probability the panel contains no women? ii. What's the probability the panel contains 3 women? iil. What's the probability the panel contains all women?The purpose of this Homework is to practice concepts covered in Chapter 9. The table below chtails the raw sample data that the researchers collected. Make sure to address all the questions in order to get a full credit. You need to show the steps on how you arrived at the final answer. Also, calculate the needed statistics in jamovi and provide tables with the relevant statistics (for #1 only). AWW Population standard deviation: 2.8 Population mean: 5.66 1) Calculate the following statistics: a. sample mean: b. sample size: c. sample standard deviation: d. sample variance: e. range: f. sample standard error of the mean: 2) For a distribution where the mean is 76 and standard deviation is 6.38, what is the probability of a raw score being between 70 and 81? 3) For a distribution where the mean is 77 and standard deviation is 6.38, what is the probability of a raw score being between 81 and 84? 4) For a distribution where the mean is 74 and standard deviation is 6.38, what is the probability of a raw score being below 64? 5) For a distribution where the mean is 73 and standard deviation is 6.38, what is the probability of a raw score being above 65?h. What's the probability the 3" woman is the 8" person in the sample? I. What's the probability the 3" woman is the 10" person in the sample? j. What's the expected position of the 3" woman in the sample