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CE 3105 - Mechanics of Fluids Laboratory

Laboratory 1 - Fluid Properties

Objectives

  • Measure density, specific gravity of various fluids
  • Measure the viscosity of a fluid

Data Aquisition

PART I - Density Measurements

  1. Measure the temperature of the fluid
  2. Weigh the beaker provided
  3. Fill the beaker with fluid, and measure its mass (beaker + fluid)
  4. Carefully measure or estimate the volume of the fluid in the beaker
  5. Repeat your measurements (3 duplicates for each fluid assigned to you)

PART II - Specific Gravity

  1. Carefully place the calibrated hydrometer into the uid and record the value corresponding to the lower meniscus),
  2. Make 3 duplicate measurements for each fluid assigned to you

PART III - Viscosity

  1. Take a steel ball (sphere) assigned to your group and note its diameter
  2. Carefully drop the ball into the ball guide
  3. Note the volume readings corresponding to the upper and lower level markers (i.e., the two rubber bands)
  4. Start the stopwatch when the ball reaches the first level marker (upperrubber band).
  5. Stop the stopwatch when the ball reaches the second level marker (lower rubber band).
  6. The density of the stainless steel sphere is 7800 $\frac{kg}{m^3}$
  7. Repeat the above steps for each sphere assigned to you

Data Analysis

PART I - Density

  1. Calculate the density of the uid by dividing the mass over volume for each fluid and sample
  2. Calculate the mean and standard deviation for the estimated density of each fluid
  3. Calculate the mass of salt present in the brackish water sample. Calculate mean and standard deviation over all samples.

PART II - Specific Gravity

  1. Tabulate the specific gravity measurements for each fluid.
  2. For each fluid calculate mean and standard deviations
  3. Plot density (calculated from PART I) (on X-axis) and specific gravity (on Y-axis). Fit a straight line and record the slope, intercept and coefficient of determination $R^2$

PART III - Viscosity

  1. Calculate kinematic viscosity for each sample using Equation 8.
  2. Use the density calculated in PART I to calculate dynamic viscosity for each sample.
  3. Compute and tabulate the mean and standard deviation for both kinematic and dynamic viscosity measurements.

Discussion/Interpretation Questions (for the Lab Report)

  1. Derive the fall velocity equation, starting from the force balance on the sphere and assuming that $C_d=\frac{24}{Re_D}$
  2. Why is it important to measure temperature when measuring density and viscosity?
  3. How do you think the density and viscosity of water would change with temperature.
  4. How do salts alter the density of groundwater? Why is measurement of brackish water density important for civil and environmental engineers.
  5. What is standard deviation?
    • What does it tell us about the accuracy of the measurements?
    • What does it tell us about the repeatability of the measurements?
  6. What are some potential sources of errors in your lab experiments. Discuss in the context of measuring density, specific gravity and viscosity.

Data Records

Part I - Gravimetric Determination of Density

Complete the table using Jupyter Notebook or Excel and cut-and-paste into the Laboratory Report

Substance Measurement ID Temp ($^o$C) Mass (Dry Beaker) Mass (Beaker + Fluid) Volume (ml) Density, $\rho$ SG (computed)
Water 1
Water 2
Water 3
Salt Water 1
Salt Water 2
Salt Water 3
Glycerine 1
Glycerine 2
Glycerine 3

Part II - Specific Gravity (by Hydrometer)

Complete the table using Jupyter Notebook or Excel and cut-and-paste into the Laboratory Report

Substance Measurement ID SG (computed from above) SG Hydrometer Reading
Water 1
Water 2
Water 3
Salt Water 1
Salt Water 2
Salt Water 3
Glycerine 1
Glycerine 2
Glycerine 3

Part III - Viscosity Determination by Stokes Law

Complete the table using Jupyter Notebook or Excel and cut-and-paste into the Laboratory Report

Team ID $d_{ball}$ $\sigma$ $\Delta V$ $d_{cyl.}$ L $t_1$(sec) $t_2$(sec) $\nu_{liq.}$ $\rho_{liq.}$ $\mu$
Team 1 $\frac{5}{32}$
Team 1 $\frac{1}{16}$
Team 2 $\frac{3}{32}$
Team 2 $\frac{1}{8}$
Team 3 $\frac{5}{32}$
Team 3 $\frac{1}{16}$
Team 4 $\frac{3}{32}$
Team 4 $\frac{1}{8}$
Team 5 $\frac{5}{32}$
Team 5 $\frac{1}{16}$
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