Solved Problems
Example
Problem: Two pipes are connected in series. Pipe 1: 100 m long, 200 mm dia, . Pipe 2: 200 m long, 300 mm dia, . Find the total head loss for a flow of 0.1 m/s.
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Example
Problem: Find the diameter of a single equivalent pipe 300 m long () that can replace the two series pipes in the previous example with the same total head loss.
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Example
Problem 3: Pipes in Parallel
Two pipes connect two reservoirs. Pipe A is long, diameter, . Pipe B is long, diameter, . The total discharge is . Find the discharge in each pipe.
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Example
Problem 4: Three-Reservoir Problem Basics
Reservoirs A, B, and C have water surface elevations of , , and respectively. They are connected at a common junction J by pipes of known lengths and diameters. How do you determine flow directions?
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Case Study 1: Redundancy in Municipal Networks
Context: Urban water supply networks use looped (parallel) systems rather than simple branching systems.
Application: A looped network ensures that water can reach any point via multiple paths. If a pipe breaks and must be isolated for repair, flow simply redistributes through other paths in the grid. This parallel arrangement also significantly reduces head losses compared to a single long pipe, maintaining higher pressures throughout the system during peak demand periods like firefighting.
Case Study 2: Water Hammer in Hydropower Penstocks
Context: Sudden changes in flow rate in long pipes cause severe pressure transients.
Application: When a turbine wicket gate closes rapidly to reject load, the kinetic energy of the water column in the penstock converts to strain energy, creating a high-pressure shock wave (water hammer) that travels back up the pipe. If not mitigated, this pressure can burst the pipe. Engineers install surge tanks (acting as an open reservoir) near the turbine to absorb this energy, allowing water to safely surge upward and reflecting the pressure wave, protecting the upstream conduit.