1. A cheap radial-vaned centrifugal fan is required to provide a supply of pressurised air to a furnace.

The specification requires that the fan produce a total pressure rise equivalent to 7.5 cm of water at a

volume flow rate of 0.2 m3

/s. The fan impeller is fabricated from 30 thin sheet metal vanes, the ratio

of the passage width to circumferential pitch at the impeller exit being specified as 0.5, and the ratio

of the radial velocity to blade tip speed as 0.1. Assuming that the overall isentropic efficiency of the

fan is 0.75 and that the slip can be estimated from Stanitz's expression, eqn. (7.34b), determine

(i) the vane tip speed;

(ii) the rotational speed and diameter of the impeller;

(iii) the power required to drive the fan if the mechanical efficiency is 0.95;

(iv) the specific speed.

For air assume the pressure is 105 Pa and the temperature is 20C.

2. The air entering the impeller of a centrifugal compressor has an absolute axial velocity of 100 m/s.

At rotor exit the relative air angle measured from the radial direction is 26360

, the radial component of velocity is 120 m/s, and the tip speed of the radial vanes is 500 m/s. Determine the power

required to drive the compressor when the air flow rate is 2.5 kg/s and the mechanical efficiency is

95%. If the radius ratio of the impeller eye is 0.3, calculate a suitable inlet diameter assuming the

inlet flow is incompressible. Determine the overall total pressure ratio of the compressor when the

total-to-total efficiency is 80%, assuming the velocity at exit from the diffuser is negligible.

3. A centrifugal compressor has an impeller tip speed of 366 m/s. Determine the absolute Mach number of the flow leaving the radial vanes of the impeller when the radial component of velocity at

impeller exit is 30.5 m/s and the slip factor is 0.90. Given that the flow area at impeller exit is 0.1 m2

and the total-to-total efficiency of the impeller is 90%, determine the mass flow rate.

Gas leaves an untwisted turbine nozzle at an angle ? to the axial direction and in radial equilibrium. Show that the variation in axial velocity from root to tip, assuming total pressure is constant, is given by

cxrsin2? constant.

Determine the axial velocity at a radius of 0.6 m when the axial velocity is 100 m/s at a radius of

0.3 m. The outlet angle ? is 45.

5. The flow at the entrance and exit of an axial-flow compressor rotor is in radial equilibrium. The

distributions of the tangential components of absolute velocity with radius are

c?1 ar b=r, before the rotor,

c?2 ar b=r, after the rotor,

where a and b are constants. What is the variation of work done with radius? Deduce expressions

for the axial velocity distributions before and after the rotor, assuming incompressible flow theory and that the radial gradient of stagnation pressure is zero. At the mean radius, r 0.3 m, the

stage loading coefficient, ? ?W/U2

t is 0.3, the reaction ratio is 0.5, and the mean axial velocity

is 150 m/s. The rotor speed is 7640 rev/min. Determine the rotor flow inlet and outlet angles at a

radius of 0.24 m given that the hub-tip ratio is 0.5. Assume that at the mean radius the axial

velocity remained unchanged (cx1 cx2 at r 0.3 m). (Note: ?W is the specific work and Ut

the blade tip speed.)

6. An axial-flow turbine stage is to be designed for free-vortex conditions at exit from the nozzle

row and for zero swirl at exit from the rotor. The gas entering the stage has a stagnation temperature of 1000 K, the mass flow rate is 32 kg/s, the root and tip diameters are 0.56 m and 0.76 m,

respectively, and the rotor speed is 8000 rev/min. At the rotor tip the stage reaction is 50% and

the axial velocity is constant at 183 m/s. The velocity of the gas entering the stage is equal to that

leaving. Determine

(i) the maximum velocity leaving the nozzles;

(ii) the maximum absolute Mach number in the stage;

(iii) the root section reaction;

(vi) the power output of the stage;

(v) the stagnation and static temperatures at stage exit.

Take R 0.287 kJ/(kg K) and Cp 1.147 kJ/(kg K).

7. The rotor blades of an axial-flow turbine stage are 100 mm long and are designed to receive gas

at an incidence of 3 deg from a nozzle row. A free-vortex whirl distribution is to be maintained

between nozzle exit and rotor entry. At rotor exit the absolute velocity is 150 m/s in the axial

direction at all radii. The deviation is 5 deg for the rotor blades and zero for the nozzle blades

at all radii. At the hub, radius 200 mm, the conditions are as follows:

Nozzle outlet angle 70

Rotor blade speed 180 m/s

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?Of a random sample of 172 elementary school educators, 118 said that parental support was the most important source of a child's success. Test the hypothesis that parental support is the most important source of a child's success for at least 75% of elementary school educators. Use a = 0.05. (a) Determine the null and alternative hypothesis. (b) Find the test statistics and P-value. (c) What is the conclusion? 4. The mean age at first marriage for married men in a New England community was 28 in 1790. For a random sample of 40 married men in that community in 1990, the sample mean and sample standard deviation of age at first marriage were 26 and 9 respectively. (a) State the hypotheses, and find the test statistics and P -value for testing whether the mean has changed. Interpret. (b) Make a decision using (c) If the decision in (b) is an error, what type of error is it, Type I of Type II?Question 1 (1 point) Random samples of size 169 are taken from an infinite population whose mean and variance are 30 and 100, respectively. Calculate the standard error of the sampling distribution of the sample mean. Round the final answer to two decimal places. Question 2 (1 point) The time it takes statistics student to write their exam is positively skewed, with a mean of 90 minutes and a standard deviation of 12 minutes. The time it takes accounting students to write their exam is a slightly negatively skewed distribution. with a mean of 95 minutes and a standard deviation of 9 minutes. A random sample of 45 statistics students and a random sample of 55 accounting students are mm selected What is the probability that the amount of time for statistics students to. write their exam will not exceed the time of accounting students to write their exam? Round the final answer to four decimal placesThe 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