7. Three charged particles are sitting in a straight line. The left-hand particle has a charge of-5.0 µC and is 8.0 cm from the middle particle, which has a charge of +3 µC. The right-handparticle is 4.0 cm from the middle-particle and has a charge of +1 µC. (a) Determine the force on the middle particle due to the left-hand particle (both magnitude and direction).[1 mark] (b) Determine the force on the middle particle due to the right-hand particle (both magntude and direction).[1 mark] Thus determine the net force on the middle particle due to both of the other particles(both magnitude and direction).[1 mark]

P4. Compute the horizontal and vertical components of the hydrostatic force on the quarter-circle panel at the bottom of the water tank in Fig.P.4 (Answer: 85.84KN, 78.84KN) (Hint: Item 3)

P1: Gate AB is Fig. P1 is 6 ft wide and weighs 2000 lb when submerged. It's hinged at B and rests against a smooth wall at A. Determine the force P at A which is needed to keep the gate closed.

The following test results were for a wastewater sample using a sample size of 100 mL. Determine the concentrations of TS, TVS, TSS, and TDS (in mg/L).3. *Tare mass of evaporating dish 54.6423 g *Dish + residue after evaporation at 105 °C 54.7173 g *Dish + residue after ignition at 550 °C 54.6893 g *Tare of What man GF/C filter 1.5347 g *Filter + residue after evaporation at 105 °C 1.5586 g *Filter + residue after ignition at 550 °C 1.5454 g

1-6: If a faucet is dripping at a rate of one drop per second and each drop contains 0.150 milliliters, calculate how much water (in liters) will be lost in 1 year.

4- The coordinates of four precipitation gauging stations are A = (3,4), B = (9,4), C =(3,12), and D = (9,12). The observed precipitation amounts at these gauges are PA = 25 mm, PB = 33 mm, PC 20 mm, PD 29 mm, respectively. These stations are located in a rectangular basin whose boundaries are defined by the following coordinates (0,0), (14,0), (14,13), (0,13). If the units of the coordinate points given above are km, compute the mean areal precipitation over this basin using: a. The Thiessen polygons method b. The arithmetic average method c. Compute the total volume of water produced by the recorded rainfall.

2. An activated sludge tank 30x30x200 ft, is designed as a plug flow reactor, with an influent BOD of 200 mg/L and a flow rate of 1mgd. a. If BOD removal is a first order reaction, and the rate constant is 2.5 days', what is the effluent BOD concentration? b. If the same system operates as a completely mixed flow reactor, what must its volume be for the same BOD reaction? c. How much bigger is this, as a percent of the plug flow volume?

1.27 a and b. The incremental rainfall data in the table were recorded at a rainfall gage on a 2-acre dirt lot. Be careful to use the 0.5-hr time step and record intensity in cm/hr. a) Plot the rainfall hyetograph. b) Determine the total storm rainfall depth in inches.

1 . \quad \Delta \mathrm{S}=\mathrm{P}-(\mathrm{E}+\mathrm{T}+\mathrm{I}+\mathrm{Q}) \text { 2. } \quad \text { Average precipitation }=\left(\Sigma \mathrm{P}_{\mathrm{i}} \mathrm{A}_{i} / \Sigma \mathrm{A}_{\mathrm{i}}\right) \text { 3. } \quad Q_{p}=C I A \text { 4. } \quad f=f_{\mathrm{c}}+\left(f_{0}-f_{\mathrm{c}}\right) \mathrm{e}^{-\mathrm{kt}} \begin{aligned} &5 \text { . }\\ &F(t)=\int_{0}^{t} f d t=f_{c} t+\left[\frac{f_{0}-f_{c}}{k}\right]\left(1-e^{-k t}\right) \end{aligned} \text { 8. } \quad H=\frac{p}{\gamma}+z+\frac{v^{2}}{2 g} \text { 9. } E=y+\frac{Q^{2}}{2 g A^{2}} \text { 10. } y_{c}=\left(\frac{q^{2}}{g}\right)^{1 / 3} \text { 11. } \frac{Q^{2}}{g}=\left(\frac{A^{3}}{B}\right) \text { 12. } \quad F_{r}=\frac{V}{\sqrt{g D}} \text { 12a. } \quad \frac{y_{2}}{y_{1}}=\frac{\sqrt{1+8 F_{r 1}^{2}}-1}{2} \text { 13. } Q=\frac{C_{n}}{n} A R_{h}^{2 / 3} S_{0}^{1 / 2} \text { 14. Area }=\frac{h}{2}\left[y_{0}+2\left(y_{1}+y_{2}+y_{3}+\ldots \ldots+y_{n-1}\right)+y_{n}\right] \begin{aligned} &15\\ &T_{R}=\frac{D}{2}+t_{p} \end{aligned} \text { 16. } \quad Q_{p}=\frac{484 A}{T_{R}} \text { 17. } \quad t_{p}=\frac{l^{0.8}(S+1)^{0.7}}{1900 y^{0.5}} \text { 18. } \quad S=\frac{1000}{C N}-1 \begin{array}{ll} 19 . & B=1.67 \mathrm{~T}_{\mathrm{R}} \end{array} \text { 20. Snyder's method } \text { 21. } \quad t_{p}=C_{t}\left(L L_{c}\right)^{0.3} \text { 22. } \quad Q p=\frac{640 C_{p} A}{t_{p}} \text { 23. } \quad \mathrm{T}_{\mathrm{b}}=3=\mathrm{t}_{\mathrm{p}} / 8 \text { 24. } \quad I-Q=\frac{\Delta S}{\Delta t} \text { 25. } \quad \frac{I_{1}}{2}+\frac{I_{2}}{2}-\frac{Q_{1}}{2}-\frac{Q_{2}}{2}=\frac{S_{2}-S_{1}}{\Delta t} \text { 26. } \quad S=K[x I+(I-x) Q] \text { 27. } \quad S_{2}-S_{1}=K\left[x\left(I_{2}-I_{1}\right)+(1-x)\left(Q_{2}-Q_{1}\right)\right] \text { 28. } \quad Q_{2}=C_{0} I_{2}+C_{1} I_{1}+C_{2} Q_{1} \text { 29. } \quad C_{0}=\frac{-K x+0.5 \Delta t}{D} \text { 30. } \quad C_{1}=\frac{K x+0.5 \Delta t}{D} \text { 31. } \quad C_{2}=\frac{K-K x-0.5 \Delta t}{D} \text { 32. } D=K-K x+0.5 \Delta t \text { 33. } \quad\left(I_{n}=I_{n+1}\right)+\left(\frac{2 S_{n}}{\Delta t}-Q_{n}\right)=\left(\frac{2 S_{n+1}}{\Delta t}+Q_{n+1}\right)

2. A municipal wastewater (Q = 6,000 m/d) having a BOD; of 250 g/m³. The water is treated by primary sedimentation before treated by a trickling filter. The primary sedimentation removes BOD5. The desired trickling filter effluent quality is 25 g/m³ of BOD5. If the filter depth is 2 m and the recirculation ratio is 1.8:1, find the required filter diameter.

10.7. The surface of a 2-ha catchment is characterized by a runoff coefficient of 0.5, a Manning's n for overland flow of 0.25, an average overland-flow length of 60 m, and an average slope of 0.5%.Calculate the time of concentration using the kinematic-wave equation. The drainage channel is to be sized for the peak runoff rate resulting from a 10-year rainfall event, and the 10-year IDF curve is given by i=150(t+8.96)0.78 cm/h where i is the average rainfall intensity in cm/h and t is the duration in minutes. The minimum time of concentration is 5 min. Determine the peak runoff rate.