Problem 1: Reynolds Number and Flow Regime

Oil with kinematic viscosity $1.8\times10^{-5}\text{ m}^2/\text{s}$ flows at $0.50\text{ m/s}$ in a $100\text{ mm}$ pipe. Determine Reynolds number and classify the flow.

Problem 2: Laminar Pipe Head Loss

Oil with density $900\text{ kg/m}^3$ and dynamic viscosity $0.25\text{ Pa}\cdot\text{s}$ flows at $0.00050\text{ m}^3/\text{s}$ through a $50\text{ mm}$ diameter, $20\text{ m}$ long pipe. Determine Reynolds number, Darcy friction factor, head loss, and pressure drop.

Problem 3: Darcy-Weisbach Major Loss

Water flows at $0.050\text{ m}^3/\text{s}$ through a $200\text{ mm}$ diameter pipe $300\text{ m}$ long. The Darcy friction factor is $0.022$. Determine velocity and friction head loss.

Problem 4: Turbulent Friction Factor using Haaland

Water flows with $Re=2.0\times10^5$ through a $300\text{ mm}$ pipe with roughness $\epsilon=0.15\text{ mm}$. Estimate the Darcy friction factor using the Haaland equation.

Problem 5: Combined Major and Minor Losses

A $150\text{ mm}$ pipe is $100\text{ m}$ long and carries $0.030\text{ m}^3/\text{s}$. Use $f=0.020$ and a total minor-loss coefficient $\sum K=6.5$. Determine total head loss.

Problem 6: Equivalent Length of Fittings

Fittings in a $200\text{ mm}$ pipe have a combined loss coefficient $K=8.0$. The Darcy friction factor is $0.020$. Determine the equivalent straight-pipe length.

Problem 7: Pipe Diameter for an Allowable Head Loss

A pipeline must carry $0.040\text{ m}^3/\text{s}$ over $500\text{ m}$ with no more than $10\text{ m}$ friction head loss. Assume Darcy friction factor $f=0.020$. Estimate the required diameter.

Problem 8: Hydraulic Grade and Pipe Pressure

A reservoir free surface has total head $50\text{ m}$ above datum. At a downstream pipe section, cumulative head loss is $12\text{ m}$, pipe elevation is $20\text{ m}$, and velocity is $2.0\text{ m/s}$. Determine the hydraulic-grade elevation, pressure head, gauge pressure, and energy-grade elevation.