Free body diagram Ма (m.g- 3πD.X. 300 M Dynamic Viscosity (W) Force x Time = shearing stress Area shearing strain Kinematic Viscosity (r) M is force involved? P No Specific

Weight (8)= pg Specific Gravity (56)= P₁₁ = X ₁²₁ 56-122 = X ²₁ Preco Vous Xp₁= 122 (8+20) Унга Fg=m-g FB +F₂-F₁ = O FB = Volvo XA₁ 3M DVE + Volus: Jay-mg = 0 F₁ = 3π D⋅V₂. ja ₂ Assume: Vt fl 9≤0 mean = average [efi] Standard deviation stdev.s[ Pesc = 0.999 3/ML = 999.0 kg/m³3 Ye₁ M₂₁ = mg - (³317 (3)) -56 Powers 3 3T D.Vz ("The Enginering Talboa com) Fluid I Left, Flui) 2 les Visors 1016 m 21.5°C tess Pleight Tamp Right more Viscons 10/6m 21.5°C Ball 2.3g 112.6 mm 8144/2 12.7mm Plastic Weight ~ Speel Bal Plastik Left twe Steet Heft tube 2.21s 1.46, 1.665 0.685 Plastic Left tube Steel Right tube 11.665 2.115 3.55 3.3, 3.45, 2.115 1.616 MyDrameter 1220 0.655 0.75 0.665 9.656 1.084 X = 9810 N/m² 3.3 at 5°C 0.999/3 3.535 0.83 0.98 0.935 0.80 0.905 CIVE 301L Aleah (she/her) Office Hours Tuesdays 12-12:50pm Wednesday 1-2 pm Looking for Mass-ball diameter-ball-Volume time + distance-velouty 8 → specific weight -H₂0 temperature Free body diagram A B distance/time Vt | MFI = A/B₂₁ = (m.g- اف 37D.X. Dynamic Viscosity (1) Forcex Time Area : shearing stress shearing strain Kinematic Viscosity (v) Assume: Ve 9-o mean = average (ulti] Standard deviation= stdev.s[] u P Fg = m. g FB +Fp-Fg=0 F3 = Volvo X2, 3MDV + Volans: 8,₁-mg = 0 F₂ = 3π D⋅ V₂.14²₂² Specific Weight (8) P9 Specific Gravity (Se P₁₁=X²₂₁ 56-12 Рась хоо →is force involved? No 1 PHOCIE (Th 86₁ Mr₁ = mg - (²377 (2)) - 56 Phones 9 3TD. VE Insert U 1 2 3 4 fx C 5 TAR Font Plastic Page Layout Formulas Data Review View Automate Developer Help 1 1 1 1 132 133 134 11 AA 2 Wrap Text 0 Conditional Format as Insert Delete Format Sort & Find & B V Merge & Center .00 Formatting Table Styles ✓ Filter Select Styles Cells Editing Tube 1 (s) 2.21 1.46 1.66 2.11 1.61 LO 34°F Mostly cloudy V data.xlsx v ESC D >/ Steel Sheet1 Accessibility: Investigate ICI F E Velocity (m/s) P S P 0.68 0.459729 1.494117647 0.209685969 S 0.06451876 0.65 0.69589 1.563076923 0.138525572 0.061672344 0.7 0.612048 1.451428571 0.157501678 0.06641637 0.66 0.481517 1.539393939 0.200197916 0.062621149 0.65 0.631056 1.563076923 0.152757652 0.061672344 FI + 0 UK F2 2 H_tube SG_1 SG_2 Mass P Volume P W Alignment # H G Dynamic Viscosity Diameter_P (D/2)^3_P SW_1 SW 2 4/3*pi = p H20@15C F3 3 171.7337573 63.38019331 Standard Deviation E Mean 1.016 m 1.084 1.22 LA Search 0.0023 kg 0.000001047 m^3 0.0126 m 2.50047E-07 F4 4 A 10623.40596 kg/(m^2*s^2) 11956.2318 kg/(m^2*s^2) 4.186666667 constant 999 kg/m^3 FS % 5 General $%9 Given 8 F Volume S Mass S Number Diameter S (D/2)^3_S Q Search A F6 T Test 6 G 1 2 3 4 5 F7 K 9.81 m/s^2 2.56048E-07 & Plastic 0.000001072 m^3 0.0084 kg 0.0127 m 7 Y Tube 2 (s) 3.55 3.3 3.45 3.3 3.53 H FB * L U 411 Cell O Steel P Dynamic Viscosity S P S P 0.83 0.28619718 1.224096386 0.336825878 0.078750839 0.30787879 1.036734694 0.313105745 0.092982918 0.98 0.93 0.29449275 1.092473118 0.327337825 0.088238892 1.27 0.313105745 0.075904423 0.8 0.30787879 0.2878187 1.128888889 0.334928267 0.085392476 0.9 F9 J M N Velocity (m/s) m"g 9 FIO 4/3 pi(D/2)^3 SG*P"g 3piDV 0.022563 1.04686E-06 10623.40596 0.054566096 0.082596625 0.072645224 0.057152167 0.074901287 H M ( FH YET! Mean L Maulick Ayden M 325.060692 84.25390966 Standard Deviation P Fia Sensitivity Q P Comments ( O Add-ins Analyze Data Add-ins DELETE BACKSPACE 4x D 1/n Learning Objectives: Recalling Understanding Applying Analyzing Evaluating Introduction: Continuum Formulation Fluid Properties Statics Force Balance` Fluid Properties Specific Gravity and Viscosity to Identify an Unknown Fluid Experimental and Theoretical Results For engineering applications, fluids are considered to be a continuum allowing engineers to apply average properties (characteristics) of the fluid in order to be able to model its behavior. Fluid properties can be dependent on temperature and pressure, specifically fluid density (p; mass per unit volume) and viscosity which is the measure of the fluid's resistance to shearing motion. A proper understanding fluid properties is essential in order to understand and/or design a system involving a fluid(s). By simple experiments, we will determine the identity of a fluid by its density and viscosity. Important Definitions Dynamic (Absolute) Viscosity (µ): the ratio of the shearing stress (T) to the rate of shearing strain, which is equivalent to the velocity gradient (ay) with dimensions: (2) Kinematic Viscosity (v): Specific Weight (y): Specific Gravity (SG or s): du dy conditions: T= fl = or N⋅s m² = = 10 poise (P). For laminar flow F.1 with the absolute viscosity divided by the density (v= dimension: (²) or (m²) = 10¹ stokes (SI); this ratio defines kinematic viscosity because force is not involved. a fluid's weight (W = mg) per unit volume; y = pg a dimensionless ratio of the density of the fluid in question to the density of a reference fluid (typically water at 4°C); SG = Р Y Po Yo Theory: Density & Specific Gravity Specific gravity (SG), and therefore density (p) can be measure using Archimedes' Principle, which states, "An object wholly or partially immersed in fluid is buoyed up by a force equal and opposite to the weight of the fluid displaced by the object." A measuring instrument that use Archimedes' Principle to determine the density (or relative density) of fluids is a hydrometer. Hydrometers are calibrated and graduated with one or more scales such as SG. Viscosity The viscosity of a fluid can be determined by performing a “Drop Test" where a sphere is allowed to move through a fluid under Stokes flow condition (see Figure F1 below). Stokes flow, or creeping flow, is a type of fluid flow where the advective inertial forces are small in comparison to the viscous forces (Reynold number, Re <<1). This typically occurs when the fluid velocities are small, the viscosity of the fluid is large, or the length-scale of the flow are very small. Where: (a) Vt g = gravitational acceleration mspher = mass of the sphere Psphe density of sphere = (b) Figure F1. (a) Kinematic Diagram and (b) Free Body Diagram As the sphere moves through the fluid the sum of the forces in in the vertical direction are equal to zero. The forces acting on the sphere include the weight force (Fw; Eq. F.2), the buoyant force (Fß; Eq. F.3), and the drag force (F; Eq. F.4) as depicted in the diagram below. Under Stokes flow condition, the drag force can be calculated using the terminal velocity (Vt). Fw = mspher 9 = (Psphere Volsphere)g = (Pspher [²²³) 9 F.2 FB Volsphere = volume of sphere D = diameter of sphere Yfluid = specific weight of fluid Pfluid density of fluid Mfluid = dynamic viscosity of fluid Fw FB = Yfluid Volfluid displaced = (Pfluid9)Volsphere = (Pfluid9) [² [D] F₁ = 3πV₂Dμƒluid FD F.3 F.4 Equipment and Materials: Glycerin-water solution with unknown % Large cylinders ● Tape ● Hydrometers (black cases; resolution = 0.001) Measuring tape (resolution = 0.01 m) Caliper (resolution = 0.01 mm) Thermometer (resolution = 0.01 °C) Stopwatch (resolution = 0.01 seconds) Steel balls (with known density) Strong magnets (to retrieve steel balls) Procedure: Specific Gravity 1. Remove a hydrometer from the case and clean it with soap and water. Dry. 2. Place the hydrometer in the fluid. If the hydrometer floats too high or sinks in the fluid, such that fluid level does not reach the graduated portion, try a different hydrometer. 3. Read the hydrometer at the fluid surface. Note the shape of the meniscus. 4. Clean and dry the hydrometer(s) before returning it to the case. Viscosity 1. Measure "fall" distance, i.e. the length between the tape marking the location to start time and end time. 2. Using the caliper, measure the diameter of the steel balls. 3. Using the thermometer, measure the temperature of the fluid. 4. Place the steel ball on free surface of fluid and release. Be careful to not drop the steel ball. 5. Using a stopwatch, start time just as the steel ball crosses the upper tape marking. 6. Stop time just as the steel ball crosses the bottom tape marking. 7. Repeat steps 4-6 ten (10) times. 8. Remove the steel balls using the magnet and clean the steel balls with soap and water. Dry. Calculations 1. Determine Pfluids from SG measurements. 2. Calculate Vs from drop length and times. 3. Calculate fluids using the equation for F₁ using V₁s and Pfluids. 4. Calculate descriptive statistics. Analysis Determine the percentage (%) of glycerin solution (use tables for theoretical density and viscosity of glycerin-water solutions provided). Provide a written description and explanation. Assignment(s): Calculations and Data Analysis Answer the following discussion questions: 1. How does temperature affect the specific gravity of fluids? 2. Describe the difference between kinematic and dynamic viscosity. How does temperature affect viscosity of fluids? 3.