Solved Problems

Example

Problem: Two pipes are connected in series. Pipe 1: 100 m long, 200 mm dia, f=0.02f=0.02. Pipe 2: 200 m long, 300 mm dia, f=0.015f=0.015. Find the total head loss for a flow of 0.1 m3^3/s.

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Example

Problem: Find the diameter of a single equivalent pipe 300 m long (f=0.02f=0.02) 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 1000 m1000 \text{ m} long, 300 mm300 \text{ mm} diameter, f=0.02f = 0.02. Pipe B is 800 m800 \text{ m} long, 200 mm200 \text{ mm} diameter, f=0.025f = 0.025. The total discharge is 0.2 m3/s0.2 \text{ m}^3\text{/s}. 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 100 m100 \text{ m}, 80 m80 \text{ m}, and 60 m60 \text{ m} 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.