Laboratory 2 Sample Protocol

Laboratory 2 Sample Protocol#

Objective#

To investigate fluid statics by measuring buoyancy forces and hydrostatic thrust, and to validate theoretical principles using experimental data.

Materials and Equipment#

  1. Quadrant balance apparatus

  2. Graduated cylinder (500 mL or larger)

  3. Thermometer

  4. Objects for buoyancy testing (rocks, composites, wood samples)

  5. Weighing scale (±0.01 g precision)

  6. Water (at ambient temperature)

  7. Ruler or measuring tape

  8. Transfer pipette

  9. Weight hangers and standard masses

Procedure#

Part 1: Displacement Volumes and Buoyancy#

  1. Prepare the Setup:

    • Measure and record the temperature of the water.

    • Fill the graduated cylinder with a sufficient amount of water. Record the initial volume level, \( V_{\text{initial}} \).

  2. Measure Object Data:

    • Weigh the first object (e.g., Rock-1) and record its mass.

    • Gently submerge the object in the water and record the new volume level, \( V_{\text{final}} \).

    • Calculate the displaced volume, \( \Delta V = V_{\text{final}} - V_{\text{initial}} \).

    • Repeat the procedure three times for each object (Rock-2, Composite-1, etc.).

  3. Repeat Measurements:

    • Repeat the displacement experiment for all six objects.

    • Ensure all measurements are consistent and record the data in a table.

Part 2: Hydrostatic Forces and Center of Pressure#

  1. Prepare the Apparatus:

    • Measure and record the water temperature.

    • Verify both tanks in the quadrant balance are empty. Trim the assembly to ensure the submerged plane is vertical.

  2. Partial Submersion:

    • Add water into the trim tank to bring the balance to the 0 position. Add weights as needed to stabilize the apparatus.

    • Gradually add water to the quadrant tank until the apparatus is level again. Record the water depth (\( h \)) and the free surface width (\( b \)).

    • Repeat the procedure for at least three trials with varying weights.

  3. Full Submersion:

    • Fully submerge the plane surface by incrementally increasing weights and adding water to balance the apparatus.

    • Record \( h \), \( b \), and the applied masses for at least three trials.

Data Analysis#

  1. Displacement Volumes and Buoyancy:

    • Calculate the buoyancy force for each object using:

      \[ F_B = \rho_{\text{water}} \cdot \Delta V \cdot g \]

    • Compare calculated object volumes with measurements from the displacement method.

  2. Hydrostatic Forces:

    • Calculate moments, \( M \), using the formula:

      \[ M = W \cdot \left( \frac{3b}{8} \right) \cdot h \]

    • Plot \( M \) vs. \( h \) for fully submerged data. Fit a straight line and compute \( R^2 \).

    • Use the slope of the line to calculate the specific weight of water and compare it to literature values.

  3. Partially Submerged Data:

    • Plot:

      \[ M + \frac{\gamma_w W R_2^2 h}{2} \quad \text{vs.} \quad h^3 \]

    • Evaluate the fit using \( R^2 \).

Deliverables#

  1. Completed data tables for Part 1 and Part 2.

  2. Plots and calculations demonstrating experimental results.

  3. A step-by-step experimental protocol with annotations for improvements.

  4. Discussion addressing:

    • Archimedes’ principle and its application.

    • Comparison of measured and theoretical buoyancy forces.

    • Analysis of hydrostatic forces and center of pressure.

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