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parallel system and determine the 0.05 m/s flow distribution for a 4 parallel pipe system when Qin D, mm 50 75 100 125 L, m 50 100 150 200 Element 0.02 0.03 0.02 0.03 2.5 Assuming that 0 is known, the unknowns in the above equations are Q1, 02, and are solved simultaneously in the manner shown in the following example. and ΔΗ H,-H, EXAMPLE 10.4 Find the flow distribution and change in hydraulic grade line for the Fig. 10.1(c) using the following data: Lı = 50 m. Di : 100 mm, K' = 2, L 75 The total discharge in the two pipes is 0-0.04 m/s parallel piping shown in Solution: Combine Eqs. (10.6) and (10.7) in the manner н, н HA HB Note that HA-HB is also an unknown, and we first solve for that value: R,= 2x981(π×0.10-4)(0.025x0510 +2)=11 980s2/m" 2x9.81(r x0.10-/4) 3x9.SIEx01A+10)4082 75 2-2x 9.81(π× 0. 152/4), (0.030×0.15 + 0.04 = 2.604 m Lastly, the flows in the two parallel pipes are computed using Eq. (10.7) lǐ980-0.0147m' V4082 0.0253 m3/s 2.604 An example of branch piping is illustrated in Fig. 10.1(d: it is made up of three elements connectasd to a single junction. Typically, the piezometric heads at locations A to Care considered to be known, and the unknowns are the discharges Qi. 02, and Q, in cach line and the piezometric head at location D Analysis proceds by assuming the direction of flow and writing the energy balance in eachel (10.8) (109) (10.10) The continuity balance at location D is 01-22-03-0 Note that a flow direction was assumed in each pipe. One method of solution is as follows: 1. Assume Ho at the junction 2. Compute Qi, Q2, and Q3 in the three branches using Eqs. (10.8) to (10.10) 3. Substitute Qi. 02, and Qs into Eq. (10.11) to check for continuity balance. Generally, the fio imbalance ΔQ = Qi-Q2-Q3 will be nonzero at the junction 4. Adjust the head HD and repeat steps 2 and 3 until AQ is within desired limits. It ma may be necessary omaboe to correct the sign in one or more of the equations if during the iterations Ho moves to or below one of the reservoirs or vice versa An alternative method of solution is to combine the equations and eliminate all of t of complexity that represents a limit using a calculator-based solution. For more complex sys except one (commonly Hp) and employ a numerical solving technique. Example 10.5 rep represents a lev

Answer 1

In this solution some basic concepts and formulas of Fluid Dynamics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.

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