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

c1 ar b=r, before the rotor,

c2 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

Gas speed at nozzle exit 450 m/s

214 CHAPTER 6 Three-Dimensional Flows in Axial Turbomachines

The Ritz Hotel has adequate room for six cabs to stack

travelers, line up, and hang tight for visitors at its passageway.

Taxis show up at the inn at regular intervals and if a taxi dri-

ves by the inn and the line is full it should drive on. Lodging

visitors require taxis like clockwork by and large and

at that point it takes a taxi driver a normal of 3.5 minutes to

load travelers and gear and leave the lodging (exhibition

nentially appropriated).

a. What is the normal time a taxi should hang tight for an admission?

b. What is the likelihood that the line will be full when a

taxi drives by and it should drive on?

Things are named tpe A, type B, type C, or type D. 22% are typeA. 47% are type B. 9% are type C, and 22% are type D. 68% of type A things are unique. 43% of type B things are unique. 88% of type C things are exceptional. 55% of type D things are uncommon.

a.) Given that a thing is unique, what is the likelihood that it is type C?

b.) Given that a thing isn't uncommon, what is the likelihood that it is typeA?

c.) Given that a thing is typeAn or type D, what is the likelihood that it is extraordinary?

A symptomatic test for a specific illness is applied to $n$ people known to not have the infection. Let $X=$ the number among the $n$ test results that are positive (demonstrating presence of the sickness, so $X$ is the quantity of bogus positives) and $p=$ the likelihood that an illness free person's test outcome is positive (i.e., $p$ is the genuine extent of test results from infection free people that are positive). Accept that lone $X$ is accessible instead of the genuine grouping of test outcomes.

a. Infer the greatest probability assessor of $p .$ If $n=20$ and $x=3,$ what is the gauge?

b. Is the assessor of section (a) fair-minded?

c. On the off chance that $n=20$ and $x=3,$ what is the mle of the likelihood $(1-p)^{5}$ that none of the following five tests done on sickness free people are positive?

@22@

The lifetime of a bulb is demonstrated as a Poisson variable. You have two bulbs types

An and B with expected lifetime 0.25 years and 0.5 years, separately. When a

bulb's life closes, it quits working. You start with new bulb of typeA toward the beginning of

the year. At the point when it quits working, you supplant it with a bulb of type B. At the point when it

breaks, you supplant with a sort A bulb, at that point a sort B bulb, etc.

1. Track down the normal absolute enlightenment time (in years), given you do precisely 3 bulb substitutions.

2. Your substitutions are presently probabilistic. In the event that your present bulb breaks, you

supplant it with a bulb of typeA with likelihood p, and with type B with

likelihood (1 - p). Track down the normal complete light time (in years),

given you do precisely n bulb substitutions, and start with bulb of typeA.

Answer for section 2 exists in shut structure as far as n and p.

(10 pts) 6 Cholesterol levels among 14-year old boys are approximately normal with mean u-170 and standard deviation 6=30 mg/dl. If we select a random sample of 36 14-year old boys and consider the distribution of the sample mean* , find: (a) the mean of ) distribution, #, (b) the standard deviation ofX distribution, or (c) the probability that sample mean * is 178 or more.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?Statistics and Sampling Distributions: S denotes the diameter of a shaft and B the diameter of a bearing, where S and B are independent with S ~ N(1, 0.0004) and B ~ N(1.01, 0.0009). (a) If a shaft and a bearing are selected at random, what is the probability that the shaft diameter will exceed the bearing diameter? (b) Assume equal variances ? = o? = o', and find the value of o that will yield a probability of noninterference of 0.95. Answers: a) 0.39 b) 0.0043Statistics Activity 2.90 12.920 2.95 3.00 3.05 3.10 Sampling Distribution of of Corresponding z 1. Grab the vertical line on the left distribution (Sampling Distribution of the Mean) and drag it until the vertical line on the right distribution (Sampling Distribution of Corresponding z) is at 1.959. What is the probability to the right of the vertical line? a. 0.05 b. 0.9750 C. 0.025 d. 0.10 -Select- 2. An analysis indicated a two-tailed critical value of z - #2.580. Approximately how much total probability would be in the tails? a. .10 b. .05 C. .025 d. .0098 -Select