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engineering problem solving computation

by | Nov 30, 2023 | questions

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ENG3103 Engineering Problem Solving Computations Semester 2, 2013 Page 1 of 6 Assessment: Assignment 2 Due: 16 September 2013 Marks: 100 Value: 10 % Question 1 (70 marks) Introduction You are designing a pipe network system that transfers water from the upper pipe to the lower pipe. Note that Figure 1 is a plan view and the elevation is constant across all pipes. The static pressure difference between points A and D is designed to be PA – PD = 3 atm (1 atm = 1 standard atmospheric pressure = 101.3 kPa). It is necessary to ensure that the speed of the flow through every pipe is at least 2 m/s so that there is no sediment build-up. Determine if this is the case. Figure 1: Plan view (looking from above) of pipe network. Theory The change in pressure between two points along a streamline (a flow path) is modelled by the Bernoulli equation 1 2 1 2 A 2 A A B 2 B B loss P ? ?V ?? gh ? P ? ?V ?? gh ? ?P (1) where P is the static pressure, ? the density, V the speed, g gravitational acceleration, h the elevation and ?Ploss is the reduction in pressure due to any losses in the system. The most important loss (and the only one to be accounted for here) is caused by friction: 2 loss 2 L V P f D ? ? ? (2) where f is the Darcy–Weisbach friction factor. Fluid flow is governed by the continuity equation (which is conservation of mass); for incompressible (constant-density) flow, this is: Q ?VA ? const (3) where Q is the volume flow rate (m3/s) and A is the cross-sectional area. Incompressible flow is a good assumption for liquids. A consequence of Eq. (3) for Eq. (1) is that if the cross-sectional area is constant for a given pipe, the flow speed at the start is equal to the speed at the end and can be defined based on the pipe ID rather than an end-point ID. Pipe networks can be considered to be equivalent to electrical circuits in series and parallel, with pressure change equivalent to potential difference and volume flow rate equivalent to current. However, the resistance cannot…

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