(a) Water is to be supplied to the Pelton wheel of a hydroelectric power plant by a pipe of uniform

diameter, 400 m long, from a reservoir whose surface is 200 m vertically above the nozzles. The

required volume flow of water to the Pelton wheel is 30 m3

/s. If the pipe skin friction loss is not to

exceed 10% of the available head and f 0.0075, determine the minimum pipe diameter.

(b) You are required to select a suitable pipe diameter from the available range of stock sizes to

satisfy the criteria given. The range of diameters (m) available are 1.6, 1.8, 2.0, 2.2, 2.4, 2.6,

and 2.8. For the diameter you have selected, determine

(i) the friction head loss in the pipe;

(ii) the nozzle exit velocity assuming no friction losses occur in the nozzle and the water

leaves the nozzle at atmospheric pressure;

(iii) the total power developed by the turbine assuming that its efficiency is 75% based upon

the energy available at turbine inlet.

3. A multi-jet Pelton turbine with a wheel 1.47 m diameter, operates under an effective head of

200 m at nozzle inlet and uses 4 m3

/s of water. Tests have proved that the wheel efficiency is

88% and the velocity coefficient of each nozzle is 0.99. Assuming that the turbine operates at

a blade speed to jet speed ratio of 0.47, determine

(i) the wheel rotational speed;

(ii) the power output and the power specific speed;

(iii) the bucket friction coefficient given that the relative flow is deflected 165;

(iv) the required number of nozzles if the ratio of the jet diameter-mean diameter of the wheel is

limited to a maximum value of 0.113.

4. A four-jet Pelton turbine is supplied by a reservoir whose surface is at an elevation of 500 m

above the nozzles of the turbine. The water flows through a single pipe 600 m long, 0.75 m diameter, with a friction coefficient f 0.0075. Each nozzle provides a jet 75 mm diameter and the

nozzle velocity coefficient KN 0.98. The jets impinge on the buckets of the wheel at a radius of

0.65 m and are deflected (relative to the wheel) through an angle of 160. Fluid friction within

the buckets reduces the relative velocity by 15%. The blade speed-jet speed ratio ? 0.48 and

the mechanical efficiency of the turbine is 98%. Calculate, using an iterative process, the loss of

head in the pipeline and, hence, determine for the turbine

(i) the speed of rotation;

(ii) the overall efficiency (based on the effective head);

(iii) the power output;

(iv) the percentage of the energy available at turbine inlet that is lost as kinetic energy at turbine

exit

6. Consider a balanced study with six subjects,

identified as A, B, C, D, E and G. In the actual

study,

? Subjects A, B and C are assigned to the

first treatment, and the other subjects are

assigned to the second treatment.

? There are exactly four successes, obtained

by A, D, E and G.

This information is needed for parts (a)-(c) below.

(a) Compute the observed value of the test

statistic.

(b) Assume that the Skeptic is correct. Determine the observed value of the test statistic for the assignment that places C, D and

E on the first treatment, and the remaining

subjects on the second treatment.

(c) We have obtained the sampling distribution of the test statistic on the assumption

that the Skeptic is correct. It also is possible to obtain a sampling distribution of the

test statistic if the Skeptic is wrong provided we specify exactly how the Skeptic

is in error. These new sampling distributions are used in the study of statistical

power which is briefly described in Chapter 7 of the text. Assume that the Skeptic

is correct about subjects C, D and E, but

in

155 SECTION 3.2 Conditional Probability and the Multiplication Rule 27. Blood Types The probability that an African American person in the United States has type Of blood is 47%. Six unrelated African American people in the United States are selected at random. (Source: American National Red Cross) (a) Find the probability that all six have type O+ blood. (b) Find the probability that none of the six have type O+ blood. (c) Find the probability that at least one of the six has type O+ blood. inmal" Evplain3.3 Multiplication rule and Independent and mutually exclusive Distinguish Between Independent or Mutually Exclusive Events Given Conditional Probability Information Question Given the following information about events A and B . P(A) = 0 . P(A AND B) = 0 . P(B) = 0.25 Are A and B mutually exclusive, independent, both, or neither? Select the correct answer below: O A and B are independent because P( A AND B) = P(A) . P(B). O. A and Bare both independent and mutually exclusive. O A and Bare mutually exclusive because P(A AND B) = 0. O A and Bare neither independent nor mutually exclusive. FEEDBACK MORE INSTR Content attribution Previous Barch FACE address assignment TOP P trend is Utility app. 1 LABELViewYou=374775 - ac Search DA STATE H... 1 014115200 MCD - PASADE... 2 TriZetto Constituent Web... ( Care3609 % Log In to Availity Use the Multiplication Rule for Conditional Probabilities Question Given that the probability of a student having an unpaid internship is 0.33, and the probability of a student having a part- time job given that the student has an unpaid internship is 0.12, what is the probability of a student having a part-time job and an unpaid internship? Enter the full answer without rounding. Sorry, that's incorrect. Try again? " Basic 5 H DOWorksheet - Probability Addition and Multiplication Rules 1. A child's board game contains a spinner with three colors: orange, yellow, and green. a. Give the sample space for two consecutive spins b. Find the probability of observing at least 1 orange. c. Find the conditional probability that the first spin is orange given that there is at least 1 orange spin. 2. The following table lists the votes of 100 senators on a health care bill in the US senate. In Favor Against Democrat 23 21 Republican 43 Independent 2 If a voter is selected at random find a. The probability the voter is a Democrat and against the bill b. The probability the voter is Republican c. The probability the voter is Republican or voted against the bill d. The conditional probability the voter is against the bill given that the voter is Democrat