Fluids

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ECPI University, Newport News *

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Mechanical Engineering

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Jan 9, 2024

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3.2 Lab Assignment: Fluids Part 1 Gauge Pressure in Fluids Initial Settings  Open PhET Simulation Under Pressure .  Stay with the default Tab showing a rectangular pool.  Check boxes: Ruler, Grid  Atmosphere: Off  Units: metric  Fill the pool to the top using the spigot.  Fluid Density and Gravity: Default values (1000 kg/m 3 and 9.8 m/s 2 )  Position the ruler so the 0 m mark is at the surface of the fluid. Preliminary exercise.  Position the pressure gauge at the very bottom of the pool.  Take the reading and multiply it by 1000 to convert it to Pa units and record it in the table below.  Imagine that you can measure the area of the bottom of the pool in square meters. Pick one of the following areas to use in your calculation: Areas: 1.14 m 2 , 1.76 m 2 , 2.29 m 2 , 3.44 m 2 , 3.95 m 2 . Record your pick.  Calculate the force exerted on the bottom of the pool using the pressure and the area values. Round your answer to the nearest whole number.  Formula and example calculation: F = PA = ( 29359 N m 2 ) ( 2.51 m 2 ) = ¿ Pressure ( Pa, N/m 2 ) Area ( m 2 ) Force (you provide the units) 29098000 1.76 51212480 This is like problem 1 in the 3.3 Practice Problem set. Simulation instructions  Drag a pressure gauge from the tool area and place the tip of the gauge at your choice of depth. Do not use 1.0 m , 2.0 m , or 3.0 m .  Move the Fluid Density slider up and down and observe how the pressure changes.  Move the Gravity slider up and down and observe how the pressure changes.  Set the sliders to any value except the default values, the extreme values of the slider, or the values used by the instructor.  Record the depth ( h ), liquid mass density ( D ), gravity ( g ), and pressure reading ( p ) in the table below.  Convert the pressure from kPa to Pa by multiplying the kPa value by 1000. 1

 Calculate the pressure using the formula p = Dgh . Round your result to the nearest whole number.  Change the units setting to Atmospheres and record the pressure.  Change the units to English and record the pressure in psi below. Depth, h ( m ) Fluid Mass Density, D ( kg/m 3 ) Gravity, g ( m/s 2 ) Pressure, p ( Pa ) 1.5m 1100 13 21.103 Gauge Pressure, p 21450 Calculated, Pa Simulation: atm Simulation: psi 21450 21103 3.061 p = Dgh =()()()= ¿ 1100 * 13 * 1.5 Change the Atmosphere setting to “on” and notice your pressure gauge go up. Place a pressure gauge at the surface of the ground. Check that the gauge pressure due to the fluid alone (pressure found in Trial 2) plus the atmospheric pressure (in the same units as your gauge pressure) adds to the reading on the gauge under the surface of the liquid. Does the shape of the container affect the pressure?  Change the tab of the PhET Under Pressure simulation to the 2 nd tab showing the two linked pools with different shapes.  Fill the pool to the top.  Place a pressure gauge at the very bottom of the pool and move it to different places along the bottom from left to right.  Answer the following question. Put an “X” in the box next to your answer. a The pressure is greatest on the left side of the pool. X b The pressure is the same at all points along the bottom. c The pressure is greatest on the right side of the pool. Part 2 Density I AM NOT ABLE TO DO LAB 2 2

Mass Density from Mass and Volume  Open the PhET Simulation Density .  Click on the middle tab (Compare).  Set the Blocks setting to Same Mass (default).  Adjust the mass slider to any value except the default value of 5.00 kg or either extreme of 1.00 kg or 10.00 kg.  Record this mass in the table below.  Measure the volume of one of the boxes (your pick) by placing the box in the water. If the box floats, click and drag the box to force it to be under the surface of the water. Note the volume meter reading on the left side of the pool and subtract 100 L from your reading. This is the volume of the box. Record the box volume in the table below.  Calculate the box mass density using the formula: D = mass Volume . Units of your answer should be kg/L. Be sure to include your units with each value in the table. D = mass Volume = ❑ ❑ = ¿  Round your density to 2 places after the decimal. Mass Volume Density Volume from Mass and Mass Density 3

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 Change the Blocks setting to Same Density .  Change the Density slider to any value except 1.0 kg/L, the default value (0.50 kg/L) or either extreme of 0.1 kg/L or 2.0 kg /L. Record this in the table below.  Pick one of the boxes and record the mass indicated on the side.  Do not pick the smallest box.  Calculate the Volume using the formula, modified from the mass density formula: V = mass massdensity = ❑ ❑ = ¿ .  Be sure to include units with your mass and volume measurements.  Check your answer by submerging the box under the water and subtract 100 L from the Volume reading on the left side of the pool. If your box floats, be sure to use the mouse to drag the box under the surface before reading the volume. Density (kg/L) Mass Volume This is like problem 3 of 3.3 Practice Problems assignment, except the practice problem uses weight and weight density and English units. Mass from Density and Volume  Leave the Blocks setting where it is (Same Density).  Change the density slider to a different value (do not use either extreme or the instructor’s value).  Record the density in the table below.  Pick a different box than in the previous part (do not use the smallest box) and measure its volume and record it below.  Substitute the density and volume into the formula for mass and record the result in the table below. This should equal the mass on the side of the box. Formula: mass = density ×volume Density (kg/L) Volume Mass This is like problem 4 of 3.3 Practice Problems Part 3: Pascal’s Principle  Open the Simulation: Pascal's Principle Lab or use the link in the assignment.  Click “Begin”.  Using the arrows, adjust the radius of tube 1 and tube 2 to equal the values listed below by your name. Student Tube 1 Radius Tube 2 Radius Instructor 44 22 4

Amin, Zahedullah 22 50 Anderson, Shane 24 48 Breeding, Matthew 26 46 Brooks, Brandon 28 44 Cotto, Sebastien 30 42 Ellison, Julius 32 40 Ferry, David 34 38 Genovese, Jacob 36 38 Leon, Bailey 36 38 Melvin, Blake 42 30 Myers, Morgan 44 28 Puttkammer, Travis 24 50 Short, Nick 26 48 Simmons, Tommy 28 46 Thompson, Davis 30 44 Velasco, An 32 46 Wayson, Cody 34 40 Williamson, Tad 36 42  Click on the pin and observe which way the balance shifts.  Replace the pin and adjust the mass amounts on the left and right to try to reduce the shift in the balance.  Repeat this process until you find masses on the left and right which result in no shift in the balance when the pin is removed. Record those masses along with the radius values in the table below.  Make a screen shot of our simulation with the pin removed to show the balance. The shot should show the mass and radius values. 5

Tube 1 Radius Mass 1 Tube 2 Radius Mass 2 26 mm 250 g 46 mm 780 g Calculate the pressure on the left and on the right. The force is the weight of the mass, converted to standard force units: 𝐹 = 𝑊 = 𝑚𝑔 = ( 𝑚𝑎𝑠𝑠𝑖𝑛𝑔𝑟𝑎𝑚𝑠 ) × 1 𝑘𝑔 1000 𝑔 × ( 9.8 𝑁 𝑘𝑔 ) The area is the area of a circle converted to square meters: 𝐴 = 𝜋 𝑅 2 = ( 3.1416 ) [ ( 𝑟𝑖𝑛𝑚𝑚 ) × 1 𝑚 1000 𝑚𝑚 ] 2 Put the results of your calculations below and calculate the pressure: p = F A Side Force Area Pressure 6

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Left (Tube 1) 2.45 0.0021 1166.667 Right (Tube 2) 7.35 0.0066 1113.636 Do not round your force calculation. Keep at least 6 figures to the right of the decimal when rounding your area. Round your Pressure to 3 places to the right of the decimal. The two pressures should be approximately the same. Practice Problem #6 of 3.3 assignment gives you both areas and the input force and asks you to calculate the output force. To solve this, start by equating the two pressures and then solve for Force 2. F 1 A 1 = F 2 A 2 Solve for F 2 à F 2 = F 1 A 2 A 1 Substitute your Force 1 and two areas from the table above to calculate the expected value of force 2. Show your substitution in the equation on the left and give your answer on the right. F 2 = F 1 A 2 A 1 =() () () 7.7 Example using instructor’s values: F 2 = F 1 A 2 A 1 =() () () = Part 4: Fluid Dynamics Lab Open Fluid Dynamics Simulation or see link in Assignment.  Click “Begin.”  Set the Left Pipe radius to any value above 15.0 cm but not the maximum.  Set the Left Pipe speed to any value above 8.0 m/s but not the maximum.  Set the Right Pipe radius to any value above 12 cm but less than the Left Pipe radius.  When the fluid moves through the pipe and readings are available, record the fluid speed through the Right Pipe and the pressure in both Left and Right.  To read the pressures, click on the meter to enlarge the view. Pipe Radius Fluid Speed Pressure Left (1) 18.3 cm 12 m/s 319 kPa Right (2) 14.7 cm 18.6 m/s 218 kPa Use the equation of continuity to predict the fluid speed in pipe 2. A 1 v 1 = A 2 v 2 7

Solve for v 2 . v 2 = v 1 A 1 A 2 Note: Formula for Area = π R 2 No need to convert units to standard units. Like units cancel in the fraction. For that matter, no need for pi. Simplified formula: 𝑣 2 = 𝑣 1 𝜋 ( 𝑅 1 ) 2 𝜋 ( 𝑅 2 ) 2 , where R stands for the radius. You must square each radius. Show the substitution into the formula of your values and calculate the result below. 𝑣 2 = 𝑣 1 ( 𝑅 1 ) 2 ( 𝑅 2 ) 2 = ( 12 ) ( 18.3 ) 2 ( 14.7 ) 2 = ¿ 1.5498 This calculation is similar to problem 5 of 3.3 Practice Problems. Problem 5 uses other units and gives you the area instead of calculating the volume. Select the correct relationship between fluid speed and pressure. a When the speed increases, the pressure increases. b When the speed increases, the pressure stays the same. X c When the speed increases, the pressure decreases. Make a screen capture of the simulation first. Include everything in the dotted line and make sure your simulation is maximum size. Make a smaller screen shot of each enlarged pressure reading, starting with the gauge on the left. 8

Simulation Enlarged Left gauge 9

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