The mean blade radii of the rotor of a mixed flow turbine are 0.3 m at inlet and 0.1 m at outlet.

The rotor rotates at 20,000 rev/min and the turbine is required to produce 430 kW. The flow

velocity at nozzle exit is 700 m/s and the flow direction is at 70 to the meridional plane. Determine the absolute and relative flow angles and the absolute exit velocity if the gas flow is 1 kg/s

and the velocity of the through-flow is constant through the rotor.

4. In a Parson's reaction turbine the rotor blades are similar to the stator blades but with the angles

measured in the opposite direction. The efflux angle relative to each row of blades is 70 from

the axial direction, the exit velocity of steam from the stator blades is 160m/s, the blade speed is

152.5 m/s, and the axial velocity is constant. Determine the specific work done by the steam per

stage. A turbine of 80% internal efficiency consists of 10 such stages as just described and

receives steam from the stop valve at 1.5 MPa and 300C. Determine, with the aid of a Mollier

chart, the condition of the steam at outlet from the last stage.

5. Values of pressure (kPa) measured at various stations of a zero reaction gas turbine stage, all at

the mean blade height, are shown in the table that follows:

Stagnation pressure Static pressure

Nozzle entry 414 Nozzle exit 207

Nozzle exit 400 Rotor exit 200

The mean blade speed is 291 m/s, inlet stagnation temperature 1100 K, and the flow angle at

nozzle exit is 70 measured from the axial direction. Assuming the magnitude and direction

of the velocities at entry and exit of the stage are the same, determine the total-to-total efficiency

of the stage. Assume a perfect gas with Cp 1.148 kJ/(kg C) and ? 1.333.

6. In a certain axial flow turbine stage the axial velocity cx is constant. The absolute velocities entering and leaving the stage are in the axial direction. If the flow coefficient cx /U is 0.6 and the gas

leaves the stator blades at 68.2 from the axial direction, calculate

(i) the stage loading factor, ?W/U2

;

(ii) the flow angles relative to the rotor blades;

(iii) the degree of reaction;

(iv) the total-to-total and total-to-static efficiencies.

The Soderberg loss correlation, eqn. (3.50) should be used

1. Consider the following random variables: The following problems involve linear combinations of X and Y. a. Compute the expectation and variance of V = X u b. Compute the expectation and variance of W = X / or c. Compute the expectation and variance of Z = . 0' (1. Compute the expectation and variance of U = W stions.pdf - Adobe Acrobat Reader DC View Window Help Tools hw5_questions.pdf X 14 4 79.6% HW5 - CEE 260 / MIE 273 Due: Friday, October 14, 11:55 PM In order to receive full credit, all work in obtaining the answer must be shown. 1. Consider the following random variables: . X: E(X) = H; var(X) = 02 . Y: E(Y) = 0; var(Y) =12 The following problems involve linear combinations of X and Y. a. Compute the expectation and variance of V = X - / b. Compute the expectation and variance of W = X/o c. Compute the expectation and variance of Z = =# d. Compute the expectation and variance of U - 2X+3Y-24 3TTheorem 1.4.11. If X is a discrete random variable with finite expectation and a is a constant, then aX has finite expectation and Efax] = aE[X]. If n 2 2 and each of the jointly distributed discrete random variables X1, . . ., Xn has finite expectation, then so does Xi + . .. + X, and EXi + . . + X] = E[Xi] + . . .+ E[X]. (1.110) The result (1.110) is particularly useful when the random variables assume only two values, 0 and 1. We define the indicator random variable 1E of the event E by