Question Solved1 Answer 3. (30P) Total head loss of between Point 1 and Point 2 in the given figure is 9 m. Water is flowing at volumetric flow rate of 0.05 m3/s in Pipe A. All pipes are made of commercial steel. The kinematic viscosity of water is 1.033x10-6 m²/s. Neglecting minor losses, find the volumetric flow rate in Pipe B. The length and diameter of pipes are given on the figure. (Note: If iteration is required, stop after the second iteration.) Pipe B L = 266 m, d = 160 mm Pipe A L = 300 m d=200 mm Pipe D L = 510 m d=250 mm Pipe C L = 190 m

Problem 2: Determine the temperatures along a 1-m horizontal rod от от described by the heat-conduction equation (k ox² ) at the time of 50 second. Assume that the right boundary is insulated and that the left boundary (x = 0) is represented by at -k' AT -|x=0 = h(T. -T.) @x where k' = coefficient of thermal conductivity (W/m . °C), h = convective heat transfer coefficient (W/m2 • °C), Ta = ambient temperature (°C), and To = temperature of the rod at x = 0 (°C). Solve for temperature as a function of time using a spatial step of Ax = 1 cm and the following parameter values: k = 2 x 10-5 mºls, k' = 10 W/m . °C, h = 25 W/m2 . °C, and Ta = 50 °C. Assume that the initial temperature of the rod is zero.

Sex Race Age 2 2 1 NNN 25 78 70 33 60 78 72 Region Ancestors astrosci educ 2 3 1 1 1 1 1 1 2 3 4 1 3 3 1 2 1 2 2 2 1 3 4 2 3 1 4 2 1 2 1 2 2 3 1 3 2 2 2 3 3 3 1 3 1 3 3 2 2 3 3 1 4 3 Income 16 34.57 15 78.65 17 56.73 18 23.46 13 54.53 13 44.23 16 66.54 16 67.85 25.67 27.87 17 55.61 16 26.54 18 76.54 16 33.46 16 23.47 NN 2 3 2 1 2 1 1 1 1 2 37 44 50 Sex= Sex of the Respondent 1=Male 2=Femal Age Age of the Respondent Race=Race of the Respondent 1= White 2=Black 3-Other Region= Region of Respondent 1= Mid West 2=Mid Atlantic 3= New England Ancestor=Do you believe that your deceased ancestors have supernatural powers? 1= Yes, Definiity; 2= Yes, Probably 3=No, Probably not; 4=no definitely not Astrosci= Is Astrology Scientific; 1=Very Scientific 2=Sort of Scientific 3= Not Scientific at all Educ=Highest Year of School completed Income=Income in 1000s of Dollars For the nominal variables race and region provide the mode and index of qualitative variation (IQV). Which variable has more variation? 2. For ordinal variables ancestor and astrosci provide the mode and median. Describe what each statistic tells you about the data. 3. For interval level variables age, education and income, provide the range, inter-quartile range, mean, median, variance, and standard deviation. Interpret each statistic. Answer the following questions: 4. Briefly explain the difference between measures of central tendency and measures of variability. Why do we need both? Can you think of a situation where central tendency might be misleading if you did not know the variability? 5. Why don't we use means for nominal level variables?

1) a) i) Define what is a vector space. ii) The 2-D Laplace equation: av av + - 0 ax? Əy? ay with appropriate boundary conditions, has a general solution of the type v(x, t) = G(x + iy) + H(x – iy) iii) Let F be a real field. Show that the general solution in part 1) a) ii) forms a vector space over F. (8 + 4 + 4 marks) = ii) The 2-D Laplace equation: a2v av + = 0 Əx2y2 with appropriate boundary conditions, has a general solution of the type v(x, t)=G(x + iy) + H(x – iy) iii) Let F be a real field. Show that the general solution in part 1) a) а ii) forms a vector space over F.

Fať 7 -6+ 62 – 4ac x = xo + vot+ v = vo + at , v2 = võ + 2aAx ,t= 2a Problem 1: A ball is thrown straight up from the ground. The ball reaches a maximum height of 5 m. For simplicity, for this problem, use g 10 m/sec. (a) Calculate the initial speed of the ball. Answer: 10 m/sec. (b) Calculate the time it takes the ball to reach the maximum height of 5 m. Answer: 1 sec. (c) Calculate the time it takes the ball to hit the ground. Answer: 2 sec. (d) Make a sketch of the position vs. time graph for this problem, y(t) vs. t. (e) Calculate the time(s) when the ball is at a height of 3 m above the ground. Answer: t = 0.37 sec and t = 1.63 sec. (f) Calculate the velocity of the ball when the ball is at a height of 3 m above the ground. Answer: v= : +6.3 m/sec for t = 0.37 sec and v -6.3 m/sec for t = 1.63 sec. =

Please can you answer the questions below with written explanations. Thank you we value your time and effort 1) a) i) Define what is a vector space. ii) The 2-D Laplace equation: a2v a2v + əx2 @y2 0 with appropriate boundary conditions, has a general solution of the type = v(x, t) = G(x + iy) + H(x – iy) iii) Let F be a real field. Show that the general solution in part 1) a) ii) forms a vector space over F. (8 + 4 + 4 marks) b) i) Explain briefly what is meant by the transpose A of a matrix A. T ii) Show that (AB)T = BIAT. iii) Hence show that (ABC)T = CTBTAT. = = iv) Give an example of a 2x2 matrix where AAT = AA-1 (3 + 6 + 4 + 4 marks)

Running speed for adult men of a certain age group is known to follow a normal distribution, with mean 6.7 miles per hour and standard deviation 1.3. Jim claims he run faster than 80% of adult men in this age group. What speed would he need to be able to run for this to be the case? Give your answer accurate to two digits past the decimal point.