Question Question 1: Water Supply and Demand Requirements (Total 15 marks) a) A small town (population 2500) is to install a new water supply system. Three possible sources of water have been identified: • A small river with adequate summer flow running through farmland Infiltration galleries or wells adjacent to the river A local creek from a small bush-clad hill catchment that has adequate total annual • Tabulate the advantages and disadvantages of each source as shown below. Advantages Disadvantages River Galleries/wells Bush-clad catchment 15 marks

Review Part A Consider the beam shown in (Figure 1). Assume A is a fixed support. Solve this problem using the basic method for constructing an influence line. Choose the correct statement about the basic method for constructing an influence line. According to the basic method, the influence line for a loading (reaction, shear, or moment) is to the same scale as the deflected shape of the beam when the beam is acted upon by the loading. To draw this deflected shape, the capacity of the beam to resist the applied loading must be removed so the beam can deflect when the loading is applied. on the member According to the basic method, the influence line can be constructed by placing the unit load at a variable position and then calculating the value of the function (reaction, shear, or moment) at the point as a function of Submit Previous Answers Correct Figure 1011 > Part B Draw the influence line for the bending moment at C Click on "add vertical line off" to add discontinuity lines. Then click on "add segment" button to add functions between the lines. Note 1 - Make sure you place only one vertical line at places that require a vertical line. If you inadvertently place two vertical lines at the same place, it will appear correct visually because the lines overlap, but the system will mark it wrong. Note 2 - Be sure to indicate the correct types of the functions between the lines, e.g, in your answer the type of a function is "linear increasing slope" for the function that actually has linear decreasing slope, the answer will be graded as incorrect. Use the button "change segment if necessary. Note 3 - Indicate the segments for all values of x shown in the diagram. Even if a segment is a constant value 0, it should be drawn in the diagram. Consider the beam shown in (Figure 1). Assume A is a fixed support. Solve this problem using the basic method for constructing an influence line. Part Draw the influence line for the vertical reaction at A. Click on "add vertical line oft" to add discontinuity lines. Then click on "add segment" button to add functions between the lines. Note - Make sure you place only one vertical line at places that require a vertical line. If you inadvertently place two vertical lines at the same place, it will appear correct visually because the lines overlap, but the system will mark it wrong. Figure No elements selected 2 m a Review Consider the beam shown in (Figure 1). Assume A is a fixed support. Solve this problem using the basic method for constructing an influence line. Part D Draw the influence line for the shear at C. Click on "add vertical line off to add discontinuity lines. Then click on "add segment" button to add functions between the lines. Note 1 - Make sure you place only one vertical line at places that require a vertical line. If you inadvertently place two vertical lines at the same place. It will appear correct visually because the lines overlap, but the system will mark it wrong. Note 2 - Indicate the segments for all values of x shown in the diagram. Even if a segment is a constant value o, it should be drawn in the diagram Figure < 1011 > No elements selected

Problems 3.2(e,f), 3.4(e,f), 3.5(b,c), 3.6(c,d), 3.10(a,b), 3.11, 3.12(b), 3.15(a,c) 140 Chapter 3 Gate-Level Minimization Problems 141 3.4 Simplify the following Boolean functions, using K-maps: (a) F(x,y, z) (2,3.6,7) (c)' F(A,B,C,D)=Σ(3,7, ll, 13, 14, 15) (e) F (w, x, y, z) = Σ(11, 12, 13, 14, 15) (g) F(w, x, y, z)=E(0.1.4,5,10,1 1,14,15) Simplify the following Boolean functions, using four-variable K-maps: (a)" F (w, x, y, z) = Σ(1, 4, 5, 6, 12, 14, 15) (b)" F (A, B, C, D) = Σ(2, 3, 6, 7, 12, 13, 14) (c) F (w, x, y, z) = Σ(1, 3, 4, 5, 6, 7, 9, 1 1, 13, 15) (d)' F (A, B, C, D) = Σ (0, 2, 4, 5, 6, 7, 8, 10, 13, i5) Simplify the following Boolean expressions, using four-variable K-maps: (a) A'B'C'D AC'D' B'CDA'BCD BCD (by (d)' (f) (h) F (A, B, C, D) = Σ(4. 6, 7, 15) F(w.rry, z)_E(2.3. I2. 13, 14, 15) F (w, x, y, z)-S(8, 10, 12, 13.4) F(w, x, y, z)-E(2.3.6.7.8.9.12,I3) UDP 02467 3.5 FIGURE 3.40 Schematic for Circuit with UDP_02467 3.6 Although Verilog HDL uses this kind of description for UDPs only, other HDLs and computer-aided design (CAD) systems use other procedures to specify digital circuits in tabular form. The tables can be processed by CAD software to derive an efficient gate structurc of the design. None of Verilog's predefined primitives describes sequential logic. The model of a sequential UDP requires that its output be declared as a reg data type, and that a column be added to the truth table to describe the next state. So the columns are organized as inputs: state: next state. (c) A'B'CD AB'D +A'BC ABCD AB'C (d) A'B'C'D' BC'D A'C'D A'BCD +ACD' Simplify the following Boolean expressions, using four-variable K-maps: 3.7 In this section, we introduced the HDLs and presented simple examples to illustrate alternatives for modeling combinational logic. A more detailed presentation of model- ing with HDLs can be found in the next chapter. The reader familiar with combinational circuits can go directly to Section 4.12 to continue with this subject. (c) AB C B'C'DBCD ACD'+ A'B'C+ A BC D Find the minterms of the following Boolean expressions by first plotting each function in a K-map: 3.8 (a) xy yz + xy'z (b) C'D+ABC ABD' +A'B'D (d) A'B A'CD B'CD BC'D VHDL-Truth Tables 3.9 Find all the prime implicants for the following Boolean functions, and determine which are essential: (a)" F(w, x, y, z) = Σ(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) (b), F (A, B, C, D) = Σ(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) (c) F (A, B, C, D) = Σ(2, 3, 4, 5, 6, 7, 9, 11, 12, 13) (d) F(w,x, y, z)=E(1.3, 6, 7, 8, 9, 12, 13, 14, 15) (e) F (A, B, C, D) = Σ(0, 1, 2, 5, 7, 8, 9, 10, 13, 15) (f) F(w, x, y, z)=E(0.1, 2, 5, 7, 8, 10, 15) Simplify the following Boolean functions by first finding the essential prime implicants: (a) F (w, x, y, z) 2(0, 2, 5, 7, 8, 10, 12, 13, 14, 15) (b) F(A, B,C, D) 2(0,2,3,5,7,8,10, 11, 14, 15) (e)* F(A, B,C,D)-(1,3,4,5, 10, 11, 12, 13, 14, 15) (d) F (w, x, y, z) = Σ(0, 1, 4, 5, 6, 7, 9, 11, 14, 15) (e) F (A, B, C, D)-Σ(0.1, 3, 7, 8, 9, 10, 13, 15) (f) F (w, x, y, z) = Σ(0, 1, 2, 4, 5, 6, 7, 10, 15) VHDL does not support truth tables directly. Instead, a truth table has to be converted into a set of Boolean equations, which can be described by signal assignment statements. PROBLEMS (Answers to problems marked with appear at the end of the text.) 3.10 1 Simplify the following Boolean functions, using three-variable K-maps: (a) F(x, y, z) = Σ (0, 2, 4, 5) (c) Fr, y, )-20,1,2,3, 5) (b) F(x,y, z)-2(0, 2, 4, 5, 6) (d) , y, z)=E(1,2,3,7) 2 Simplify the following Boolean functions, using three-variable K-maps: (b)" F(x, y, z) = Σ(1, 2, 3, 6, 7) (d) F(x, y, z) = Σ( 1, 2, 3, 5, 6, 7) (f) F(x, y, z)=E(3, 4, 5, 6, 7) (a)" F(x, y, z) = Σ (0, 1, 5, 7) (c) Fx,y, z) (2,3,4,5) (e) P(x, y, z) = Σ(0,2,4,6) Simplify the following Boolean expressions, using three-variable K-maps: (a)'. F (x.yz) = xy + x'y'z, + χ,yz (c)" F (x, y, z) = x,y + yz' + y,z' 3.11 Using K-maps for Fand F,convert the following Boolean function from a sum-of-prod- 3.3 ucts form to a simplified product-of-sums form. (d) F(x, y, z) = x,yz + xy,z' + xy'z F(w ryz)0,,2, 5,8, 10, 13)

Please help solving problem 1,2 and 3. Thank you very much. For questions 1 - 3, consider the following test results obtained for a surface water sample. lon Concentration (ppm) Ca2+ 36.0 Mg2+ 10.8 Na 12.4 K 5.9 нсоз" 82.1 SO42 32.0 CI 16.9 NO3 7.4 1. Check the accuracy of the analytical measurements. Do you suspect that a constituent of significance has been neglected? If so, is it a cation or an anion? 2. Determine the mole fraction of calcium, magnesium, and sulfate for the water sample given above. 3. Determine this water's hardness and alkalinity in mg/L as CaCO3.

Die-rolling experiment: 1) Acquire any "fair-enough" die. 2) Roll it at least 100 times (each person for themselves). 3) Note what the outcome is overy time. 4) For each group of 5 (go consecutively, i.e. group first five rolls, then the next five rolls, etc.), take the average of the 5 rolls. For example, if the first five rolls are \( 3,6,1 \), 5 , and 3 , Die-rolling experiment: 1) Acquire any "fair-enough" die. 2) Roll it at least 100 times (each person for themselves). 3) Note what the outcome is overy time. 4) For each group of 5 (go consecutively, i.e. group first five rolls, then the next five rolls, etc.), take the average of the 5 rolls. For example, if the first five rolls are \( 3,6,1 \), 5 , and 3 , the average will be \( 18 / 5=3.6 \). 5) You will end up with at least 20 averages. Plot these averages on a \( 2 \mathrm{D} \) column graph. Alternatively, you can do a histogram of your results, which will be a fancier way of doing a 2D column graph. With a histogram though, you can control the bin size and instead of each individual average (e.g. 3.2, 3.4. 3.6, etc.). you can group them together with a bin size of 1 . Bonus credits will be assigned to those showing their results with a histogram of bin size 1 in addition to their regular \( 2 \mathrm{D} \) column graphs. 6) All the probabilities of \( 1,2,3,4,5 \) and 6 are \( 1 / 6 \) with a fair die. Therefore, the probabilities are said to be "uniformly distributed". Then, why is your \( 2 D \) column graph / histogram not looking uniform at all? Speculate / comment on the rationale for this.

2-4 Estimate the TDS for one of the water samples in Problem \( 2-1 \) or \( 2-2 \) (to be selected by instructor) using Eq. (2-11) and by summing the mass of the individual ionic species. How do the computed values compare?The following test results were obtained for three treated wastewater effluent samples. Check the accuracy of the analytical 2-4 Estimate the TDS for one of the water samples in Problem \( 2-1 \) or \( 2-2 \) (to be selected by instructor) using Eq. (2-11) and by summing the mass of the individual ionic species. How do the computed values compare?The following test results were obtained for three treated wastewater effluent samples. Check the accuracy of the analytical measurements for one of the waters (to be selected by instructor). Do you suspect that a constituent of significance has been neglected? If so, is it a cation or anion? Determine the mole fraction of \( \mathrm{Ca}^{2+}, \mathrm{Mg}^{2+} \), and \( \mathrm{SO}_{4}^{2-} \) for one of the following treated wastewater effluents (to be selected by instructor).

Which of the following statements is correct regarding Kepler's three laws of planetary motion? Angular momentum of any planet about an axis through the Sun and perpendicular to the orbital plane is not invariant during its motion. Planets move in elliptical orbits with the sun not being at its center. Orbital period of a planet is directly proportional to Which of the following statements is correct regarding Kepler's three laws of planetary motion? Angular momentum of any planet about an axis through the Sun and perpendicular to the orbital plane is not invariant during its motion. Planets move in elliptical orbits with the sun not being at its center. Orbital period of a planet is directly proportional to its distance from the sun. Kepler's laws are valid only for planets in the solar system.