15 - Bernoulli Assignment Sheet
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Bernoulli’s Equation Simulation Lab Assignment
Tanyitaku tanyi
https://phet.colorado.edu/en/simulation/legacy/fluid-pressure-and-flow
Please answer all questions.
You may input answers directly into this Word document. For the equations and calculations for the Water Tower, Problem 4, you may either scan them in, take a digital picture and insert it, or use equation editor – your choice.
Directions: For the Flow Tab: (In this simulation, the flow rate out of the pipe at the left end is kept at a constant value shown in the box in the upper left corner.)
1.
With the friction box unchecked, check the box for flux meter to place a flux meter in the middle of the pipe. Move the speed gauge to different locations inside the pipe to take speed reading. What do you find from the speed gauge? A. The speed gauge consistently registers 1.6 m/s regardless of the location. Thus, the speed remains constant throughout the tube due to the presence of friction.
2.
Now use a handle in the middle to make the pipe narrower in the middle. Record the readings of the flux meter: Flow rate: 50,000L/s
, area
: 0.8 m^2, (flux: Ignore this read ing and the way “flux” is used in this simulation because the term "flux" can be ambiguous.). Which of these quantities stayed the same when you change the size of the pipe and why? Please also move the speed gauge around to see how the speed varies at different locations inside the pipe.
A. Despite altering the pipe size, the flow rate remained consistent. This consistency arises because the volume remains constant. Although reducing the pipe's radius affects speed and pressure, adjustments in distance compensate to maintain a constant flow rate. However, there is an observed change in area.
The speed changes inside the pipe but stays steady at 1.6 m/s, but it increases when the pipe narrows the speed does increase to 6.2 m/s. But, after making the pipe bigger the speed drops down again.
Adapted from Fluid Pressure and Flow Phet Simulation worksheet, Yau-Jong Twu. http://phet.colorado.edu
3.
What do you think will happen qualitatively
to these 2 readings of the flux meter if you use a
handle in the middle to make the pipe wider in the middle? Flow rate: stays the same, area: increases . Do the actual readings match your expectations? Please also move the speed gauge around to see how the speed varies at different locations inside the pipe. Briefly write down your observations. A. Indeed, the flow rate remained constant at 5000 L/s, and the area increased to 6.4 m^2, aligning with my expectation. As anticipated, the speed decreased with the increased radius, dropping from 1.6 m/s to 0.8 m/s.
4.
Click “Reset All” and then check both the friction and the flux meter boxes. Move the speed
gauge different locations inside the pipe to take speed reading. What do you find from the speed gauge? A. the flow rate remained constant at 5000 L/s, and the area increased to 6.4 m^2, aligning with my expectation. As anticipated, the speed decreased with the increased radius, dropping
from 1.6 m/s to 0.8 m/s.
5.
Now change the fluid to honey and then to gasoline. For each type of fluid, move the speed gauge to different locations inside the pipe to take speed reading. What do you find from the speed gauge? Explain your observations. A. The speed remained consistent at 1.6 m/s in the middle of the pipe and 0.8 m/s on the sides, indicating no change. Thus, it can be inferred that density had no impact on the flow rate or speed.
Adapted from Fluid Pressure and Flow Phet Simulation worksheet, Yau-Jong Twu. http://phet.colorado.edu
For the Water Tower Tab
:
1.
Click “Fill” to fill the tower with water. Then open the red cover at the bottom of the tank and observe the trajectory of the water coming out of the opening. You may wish to use the speed meter and ruler to measure the speed of water flow at various locations and the depth of water or the horizontal displacement of the water flow. Briefly explain how the path of water flow changes as the water level in the tank goes down. A. As the tank begins to empty, both the flow rate and the horizontal trajectory decrease. Additionally, the horizontal displacement also diminishes.
2.
Click “Hose” to connect a hose to the water tank. Click “Match leakage” on the giant faucet on the top left and then click “Fill”. Then open the red cover at the bottom of the tank. How does the maximum height of the water flow compare to the water level in the tank? A. The maximum height of the water flow exceeds the fill height of the tank. This relationship persists even when the fill height is adjusted; there is no change observed.
3.
Now use the brown knob at the opening of the hose to adjust the angle at which water comes
out. When water comes out at an angle (instead of going straight up), water does not shoot as
high as before. Explain your observations qualitatively. A.
When the water is angled, it doesn't reach the same height as when it's positioned vertically. The introduction of horizontal displacement reduces the pressure, resulting in a lower trajectory for the water.
4.
Use the ruler and speed meter to take some measurements for the surface of the water inside the tank and the stream of water at its minimum height (with the hose at an angle). Plug these numbers into Bernoulli’s equation to see whether Bernoulli’s equation holds true in this case: A.
v2x^2 = v1x^2 + 2 g ( h1 – h2 )
(22.1 m/s)2 = (14.0 m/s)2 + (2)(9.8 m/s2 )(15.00 m – 0.00 m)
(12.5 m/s)2 = (14.0 m/s)2 + (2)(9.8 m/s2 )(15.00 m – 17 m)
vy^2 = √(2gh)
17.15 m/s = √(2)(9.8 m/s)(15.00 m)
18.25 m/s = √(2)(9.8 m/s)(17 m)
Adapted from Fluid Pressure and Flow Phet Simulation worksheet, Yau-Jong Twu. http://phet.colorado.edu
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vx^2 + vy^2 = vz^2
(14.0 m/s)^2 + (17.15 m/s)^2 = (22.1 m/s)^2
(12.5 m/s)^2 + (18.25 m/s)^2 = (22.1 m/s)^2
5.
Now use the brown knob to adjust the hose so the stream of water shoots straight upward again. Click “Manual” on the giant faucet on top left, so the faucet turns off. Compare the water level in the tank to the maximum height of the stream of water as both of them go down. Why is the maximum height of the water stream always a little taller than the water level in the tank? A. As the water level inside the tank decreases, the maximum height of the water also decreases. However, it's worth noting that the water always remains slightly higher. This phenomenon can be explained by Bernoulli's equation, which dictates that to conserve energy, the stream must be at the same height above the water level in the tank.
Adapted from Fluid Pressure and Flow Phet Simulation worksheet, Yau-Jong Twu. http://phet.colorado.edu