The average velocity of blood flowing in a certain 4 mm diameter artery in

the human body is 0.28 m/s. Calculate the Reynolds number and determine

whether the flow is laminar or turbulent. The viscosity and density of blood are

approximately 4 cP and 1.06 Mg/m3

, respectively.

P6.16

(a) Determine the volumetric flow rate of blood in the artery of P6.15.

(b) Calculate the maximum velocity of blood across the artery's cross section.

(c) Determine the amount by which the blood pressure decreases along each

10 cm length of the artery.

P6.17

The Boeing 787 Dreamliner is designed to be 20% more fuel efficient than the

comparable Boeing 767 and flies at an average cruise speed of Mach 0.85. The

midsize Boeing 767 has a range of 12,000 km, a fuel capacity of 90,000 L, and flies

at Mach 0.80. Assume the speed of sound is 700 mph, and calculate the projected

volumetric flow rate of fuel for each of the two Dreamliner engines in m3

/s.

P6.18

Assume that the fuel lines for each engine in the Boeing Dreamliner of P6.17

are 7/8 in. in diameter and that the density and viscosity of jet fuel are 800 kg/

m3

and 8.0 10?3

kg (m s), respectively. Calculate the average velocity of the

fuel in m/s and the Reynolds number of this flow. Also determine whether the

flow is laminar or turbulent.

P6.19

(a) For a 1.25 in. diameter pipe, what is the maximum volumetric flow rate

at which water can be pumped and the flow will remain laminar? Express

your result in the dimensions of gallons per minute.

(b) What would be the maximum flow rate for SAE 30 oil?

P6.20

At any time, approximately 20 volcanoes are actively erupting on the Earth, and

50-70 volcanoes erupt each year. Over the past 100 years, an average of 850

people have died each year from volcano eruptions. As scientists and engineers

study the mechanics of lava flow, accurately predicting the flow rate (velocity) of

the lava is critical to saving lives after an eruption. Jeffrey's equation captures

the relationship between flow rate and viscosity as:

V 5 rgt2 sin (a)

3m

1. The following table shows the the joint probability mass function of the discrete random variables X and Y: Y X 2 (a) Find the marginal probability mass function of X: Fx (x). (b) Find the marginal probability mass function of Y: Fy(y). (c) Is X independent with Y? Explain why.1) X and Y are discrete random variables with a joint probability mass function that is given by: p_(X, Y}(0,0) = 0.15 P_{X, Y}(0,1) = 0.20 P_{X,Y}(1,0) = 0.30 P_{X, Y}(1,1) = K The probability mass function is 0 for all other values of (x,y). (a) What is the value of the constant K? (b) What is the probability that X = 1 and Y = 0? (c) What is the probability that X = 1 given that Y = 0? (d) Find the probability mass function of X. (e) Find the probability mass function of Y. (f) Are X and Y independent? Why or why not? (g) Find the conditional probability mass function of X given Y. (h) Find the conditional probability mass function of Y given X. (i) Find the conditional expectation of X given that Y = 0. () Find the expected value of X. (k) Find the expected value of Y.3. Figure 1, below, shows the probability mass function, fy(y), of Y fy (y) 0.4 0.3 0.2 0.1 -1 0 2 y Figure 1: Probability mass function for Question 3 (a) Use the information in Figure 1 to complete the probability mass function, fy(y), of Y. ... ify= ... if = . .. fy(y) = if y = ... ify= . .. 0 otherwise (b) Find P(Y