What is meant by the term nominal design in connection with a radial flow gas turbine rotor? Sketch

the velocity diagrams for a 90 IFR turbine operating at the nominal design point. At entry to a 90

IFR turbine the gas leaves the nozzle vanes at an absolute flow angle, ?2, of 73. The rotor blade tip

speed is 460 m/s and the relative velocity of the gas at rotor exit is twice the relative velocity at rotor

inlet. The rotor mean exit diameter is 45% of the rotor inlet diameter. Determine,

(i) the exit velocity from the rotor;

(ii) the static temperature difference, T2 - T3, of the flow between nozzle exit and rotor exit.

Assume the turbine operates at the nominal design condition and that Cp 1.33 kJ/kg K.

10. The initial design of an IFR turbine is to be based upon Whitfield's procedure for optimum efficiency. The turbine is to be supplied with 2.2 kg/s of air, a stagnation pressure of 250 kPa, a stagnation temperature of 800C, and have an output power of 450 kW. At turbine exit the static

pressure is 105 kPA. Assuming for air that ? 1.33 and R 287 J/kg K, determine the value

of Whitfield's power ratio, S, and the total-to-static efficiency of the turbine

2. Let X be a multivariate random variable (recall, this means it is a vector of random variables) with mean vector p E R" and covariance matrix 22 e Rm\". Let 2 have one zero eigenvalue. Prove the space where X takes values with non-zero probability (this space is called the support of X) has dimension n 1. How could you construct a new I? so that no information is lost from the original distribution but the covariance matrix of X has no zero eigenvalues? What would I? look like if E has m S :1 zero eigenvalues? Hint: use the identity Vang: K) = i i Cov(Y,~, Y 3-). i=1 i=lj=1 \fConsider a multivariate random variable (X1 , X2, X3) with parameters 71 0 3 72 0.5 73 -0.2, and N = 30 Calculate the following () EX Number (b) var( X ) Number (c) cov( X1, X2) = NumberGannon University Department of Mechanical Engineering GENG 623, Fall 2016 Extra Credit Problem (5%) Due Date: October 27, 2016 Consider a linear function of the four multivariate - Normal random variables: A -d,+ a,X, + a,X, + a,X, + a,X. A is linear function of Multivariate-Normal random variables and X, . ... . X, are Normal random variables with a mean of ( and standard deviation of 1. Show that sumproduct of linear coefficients represents covariance of Multivariate-Normal random variables. Covar( A, A ) = E((a,a,) + (a,a,) + (a,a,) + (a,a))