Problem 1: Velocity-Area Method (Mid-Section Method) A stream cross-section is divided into three vertical segments to measure discharge.

Problem 2: Estimating Mean Velocity using the 2-Point Method A hydrologist is measuring flow in a deep river segment. The total depth of the segment is $4.0 \text{ m}$. Using a current meter, the velocity measured at $0.8 \text{ m}$ below the surface is $1.2 \text{ m/s}$, and the velocity measured at $3.2 \text{ m}$ below the surface is $0.6 \text{ m/s}$. Calculate the estimated mean velocity of the vertical profile.

Problem 3: Stage-Discharge Relationship (Rating Curve) A river gauging station has an established stage-discharge rating curve defined by the equation $Q = 15(G - 0.5)^{1.5}$, where $Q$ is the discharge in $\text{m}^3\text{/s}$ and $G$ is the gauge height (stage) in meters. The constant $0.5$ represents the gauge height of zero flow ($a$). If the current stage reading is $2.5 \text{ m}$, calculate the estimated discharge.

Case Study 1: The Importance of Rating Curve Calibration A severe flash flood occurs on a river, resulting in extreme high flows that scour the riverbed and alter its cross-section. Discuss why the hydrologist must immediately perform new current-meter measurements after the flood waters recede, rather than relying on the existing rating curve.

Case Study 2: Advancements in Discharge Measurement (ADCP vs. Current Meters) Historically, discharge was measured manually by wading into a stream with a mechanical current meter. Today, Acoustic Doppler Current Profilers (ADCPs) are widely used. Discuss the technological advantages of using an ADCP for streamflow measurement.