CE 3105 - Mechanics of Fluids Laboratory

Laboratory 2 - Fluid Statics

Objectives

  • Understand the fluid statics and forces on a body
  • Measure the buoyancy force on a number of objects
  • Determine the hydrostatic thrust acting on a plane surface immersed in water when the surface is fully submerged

Data Acquisition

Part 1 Displacement Volumes and Weights

  1. Measure the temperature of the water
  2. Fill a graduated cylinder with water, record initial volume level
  3. Weigh the object #1
  4. Immerse object #1 in the water, record the new volume level.
  5. remove the object and record the volume displaced
  6. Repeat three times with each object (three objects in total - 9 measurements)

Part 2 Center of Pressure

  1. Measure the temperature of the water
  2. Before each experiment make sure both tanks are empty and trim the assembly to bring the submerged plane to the vertical.
  3. Add water into the trim tank (using the transfer pipette) until the balance reaches the 0 position. You may need to add one of the weight hangers and a few masses to help trim the assembly.
  4. Add additional weights. Use the second weight hanger if appropriate. Add water into the quadrant tank until the apparatus is level again. Record the additional weights and the level of the water ($h$). Use a ruler to measure the distance to the outer edge of the water surface from the planar surface (the "length" of the free surface, $b$).
  5. Repeat the procedure for a full range of weights (at least 3 measurements for partially submerged and fully submerged cases)

Data Analysis

Part 1

  1. Obtain the density of water and other materials used in the lab for the measured temperature from a reputable source (textbook, web). Note the citation
  2. Calculate the volume of displaced water, $\Delta V$, for all objects
  3. Determine the buoyancy force, $F_B$, on each object
  4. For fully submerged objects, calculate the volume of the object based on displacement.
  5. Use the measured mass and the density of the object to calculate the volume of the objects. How do they compare with volumes measured using water displacement?
  6. For the floating object-Calculate the mass of the objectusing Archimedes principle. How does this mass compare to the measured value?

Part 2

  1. Calculate moment (M) for generated by each applied weight.

  2. Using the $\sum{M} = 0$ principle calculate the approximate vertical force for each set of measurements. This force acts at a distance of $\frac{3b}{8}$ from the planar surface. While this is strictly true only for partially submerged conditions; it is a first-order approximation for the fully submerged case as well.

  3. Plot moment M ($Nm$) vs. height of depth of liquid, $h$ (m) for the fully submerged dataset. Fit a straight line and compute the coefficient of determination $R^2$.
  4. Use the slope of the line from previous step - which is equal to $- \frac{\gamma_w W}{2}(R_2^2-R_1^2)$. Using R1 = 100 mm and R2= 200 mm, calculate the weight of water per unit volume ($\gamma_w$). Compare this value to the specific weight reported in the literature for the measured temperature.
  5. For the partially submerged dataset plot $M + \frac{\gamma_w W R_2^2 h}{2}$ versus $h^3$. Fit a straight line and evaluate the adequacy of the fit using the coefficient of determination $R^2$.

Discussion/Interpretation

  1. What is Archimedes principle?
  2. A rock is thrown in a beaker of water and it sinks to the bottom. Is the buoyant force on the rock greater than, less than, or equal to the weight of the rock? Explain your answer
  3. An embankment that is 50 m high x 20 m wide is to be constructed to hold water. Assuming the embankment is to be constructed using concrete of density 2600 $\frac{kg}{m3}$, what is the minimum thickness necessary to withhold the water when full such that there is no over-turning. Assume the embankment is a cuboid. Hint: the moment exerted by the embankment at the bottom must balance the moment exerted by the water.

Data Records

Part-1

Material $V_{initial}$ $V_{final}$ $\Delta V$ $V_o$ geometry $V_o$ displacement mass submerged(yes/no)
Rock-1
Rock-2
Composite-1
Composite-2
Wood-1
Wood-2

Part-2 (Partial Submerge)

Trial mass (grams) $h$ mm $b$ mm
1
2
3
4
5

Part-2 (Fully Submerge)

Trial mass (grams) $h$ mm $b$ mm
1 180
2 180
3 180
4 180
5 180

References

  1. Laboratory 2 circa 2021
  2. Descriptive Statistics
  3. Plotting Data
  4. Fitting Data Models
  5. This page as Jupyter ipynb file
  6. Holman, J.P., (2012) Experimental Methods for Engineers, 8th Ed. (Chapters 1-3)
  7. Holman, J.P., (2012) Experimental Methods for Engineers, 8th Ed. (Chapter 15 Report Writing)
  8. Laboratory 2 Example Report

Videos

  1. Laboratory 2 Video by Dr. Uddameri
In [ ]: