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02 and both may safely be ignored in practice. 2 Energy losses in pipe flow L Darcy-Weisbach equation V L V2 hf � � D 2g D 2 1 where hf is the energy head loss, L is the pipe length, D is the diameter and V is the mean velocity. com 42 Concise Hydraulics Pipe Flow The friction factor���is dimensionless and can be derived by experiments or from the following chart or formulas. 3 m/s. 8�10-2 kg/ms and �=800kg/m3, calculate (a) the pressure drop in a 45 m length and the maximum velocity, and (b) the velocity 5mm from the pipe wall.

1 Background Hydraulic modelling includes physical and mathematical models. Initially, due to a lack of computing power, physical models dominated the hydraulic modelling field. Froude (1870) established the famous Froude similarity when he was testing a ship model. In 1885, Reynolds built a river model for Mersey based on the Froude similarity. The Buckingham’s Pi theorem (by J. Buckingham in 1914) extended the similarity principle to a broader sense. Since then, physical models have been widely used in hydraulics, including complex 3D river models with sediments.

5 Combination of pipes 1) Pipes in series Two or more pipes of different sizes or roughnesses are so connected that fluid flows through one pipe and then through the others in turn. com 45 Concise Hydraulics Pipe Flow H � � local loss � h f 1 � hf 2 Q1 � Q2 2 1 H 2) Pipes in parallel The flow is divided among the pipes and then is joined again. Q � Q1 � Q2 � Q3 Energy loss in pipe 1 = Energy loss in pipe 2 = ... A B 3) Networks of Pipes Problems on networks of pipes in general are complicated and require trial solutions in which the elementary circuits are balanced in turn until all conditions for the flow are satisfied.

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