Solve

(a) On one chart, plot the flow velocity in mph as a function of the slope,

varying the slope from 0 to 90.

(b) On the other chart, plot the flow velocity in mph as a function of the flow

thickness, varying the thickness from 0 to 300 cm.

(c) Discuss and compare the influence of the slope and the thickness on the

flow velocity.

P6.22

A steel storage tank is filled with gasoline. The tank has partially corroded on its

inside, and small particles of rust have contaminated the fuel. The rust particles

are approximately spherical, and they have a mean diameter of 25 mm and

density of 5.3 g/cm3

.

(a) What is the terminal velocity of the particles as they fall through the

gasoline?

(b) How long would it take the particles to fall 5 m and settle out of the liquid?

P6.23

A small water droplet in a mist of air is approximated as being a sphere of

diameter 1.5 mil. Calculate the terminal velocity as it falls through still air to

the ground. Is it reasonable to neglect the buoyancy force in this instance?

P6.24

In a production woodworking shop, 50 mm spherical dust particles were blown

into the air while a piece of oak furniture was being sanded.

(a) What is the terminal velocity of the particles as they fall through the air?

(b) Neglecting air currents that are present, how long would it take the cloud

of sawdust to settle out of the air and fall 2 m to the ground? The density

of dry oak is approximately 750 kg/m3

.

1. Suppose (X, Y, Z) follow the multivariate normal distribution: 1 0.4 0.2 ( X , Y, Z ) ~ N 3 0.4 1 0.3 (2) 0.2 0.3 1 (a) Find the distribution of X + Y + Z; (b) Find Cov(2X - 3Y + Z, X + Y - Z). Hint for 1.: A linear transform of a univariate/multivariate normal r.v. is a univariate/multivariate normal random variable. A univariate/multivariate normal random variable is entirely characterized by its mean and its variance / covariance matrix.1. Let Y be a discrete random variable with probability mass function 1/ = 0, 1,2, ... elsewhere a) Prove that the above is a probability mass function satisfying all the required conditions. b) Show that E(Y) = 1.known as a 10. A random variable that may take on any value in an interval or collection of intervals is a. continuous random variable. b. discrete random variable. c. mixed type random variable. d. multivariate random variable. e. none of the above 11. Which of the following is a required condition for a discrete probability function? a. [f(x) =0 for all values of x b. f(x) 21 for all values of x c. f(x)