Solved Problems

Example

Problem: Oil (SG=0.85SG=0.85, ν=1.8×10−5 m2/s\nu = 1.8 \times 10^{-5} \text{ m}^2/s) flows through a 100 mm diameter pipe at 0.5 m/s. Determine the flow regime.

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Example

Problem: Water flows at 2 m/s through a 150 mm diameter cast iron pipe (ϵ=0.26\epsilon = 0.26 mm). The pipe is 50 m long. Calculate the head loss. Use ν=10−6 m2/s\nu = 10^{-6} \text{ m}^2/s.

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Example

Problem 3: Reynolds Number and Flow Regime Water at 20∘C20^\circ\text{C} (kinematic viscosity ν=1.0×10−6 m2/s\nu = 1.0 \times 10^{-6} \text{ m}^2\text{/s}) flows through a 50 mm50 \text{ mm} diameter pipe. What is the maximum flow rate for the flow to remain laminar?

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Example

Problem 4: Hazen-Williams Equation Calculate the head loss in a 1 km1 \text{ km} long, 200 mm200 \text{ mm} diameter cast iron pipe (C=130C = 130) carrying water at 50 L/s50 \text{ L/s}.

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Case Study 1: Oil Pipelines and Temperature Effects

Context: Pumping crude oil over long distances presents unique challenges compared to water.
Application: Crude oil viscosity is highly sensitive to temperature. In cold environments like Alaska, oil pumped through the Trans-Alaska Pipeline must be kept warm to maintain a low viscosity and turbulent flow, minimizing friction losses and pumping power required. If the flow stops and cools, the oil's viscosity skyrockets (potentially acting like a Bingham plastic), requiring massive pressure to restart the flow. Insulation and heating stations are critical design features.

Case Study 2: Water Distribution Network Aging

Context: The friction factor of pipes changes over their lifespan.
Application: Over decades, cast iron and steel pipes develop internal tuberculation and scaling, which significantly increases their relative roughness. This raises the friction factor (ff in Darcy-Weisbach or lowers CC in Hazen-Williams), leading to increased head losses. Municipalities often find that aging networks can no longer deliver the required pressure for firefighting or peak demand. Engineers must model these aged pipes correctly to plan for rehabilitation, such as cleaning and cement-mortar lining, or full replacement.
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