Calibration of a Pressure on a Submerged Surface
David Willis
Matthew Gleason
Justin Wallace
Mechanical Engineering Department
THERMAL FLUIDS LAB
MEEN 317.012
13th SEPTEMBER 2018
ABSTRACT
In this experiment, containing two separate activity’s which both relate to Bernoulli’s equation and the continuity equation through physical representation. In the first activity weight is applied to one side on a piston with a known weight and area. From this you see the pressure that the weight applied gives. Also, once the weights have been applied in an increasing manner there should be energy stored in the system due to Bernoulli’s principle. For the second experiment had similar details, but was done on a hydrostatic bench. There is a known surface area of a submerged object that pivots on an arm where weights can be applied to counteract the force of buoyancy. For both experiments weights were applied in an increasing and then decreasing manner. The raw data that was collected was to be used to see if the experiment had logical reasoning behind the collected data.
Introduction and Background
For this experiment both of the devices used needed to be calibrated before being used for the most accurate data. The two devices used were the Bourdon Pressure Gauge and the other was the Armfield Hydrostatic Pressure Apparatus. The device mention was to measure the dead weight pressure and the second was to measure the center of pressure for a submerged surface. For the bourdon pressure gauge the overall scope is that when a known weight is placed on the piston that has a known area you are able to determine pressure with the gauge on the device and thus can find the force. The other apparatus (Hydrostatic pressure apparatus) other all scope is that with a pivot arm that pivots on knife edges and they coincide with the axis of the quadrant. Thus, of the hydrostatic forces acting on the quadrant when immersed, only the force on the rectangular face end gives rise to a moment about the knife edge axis.

Theory
Experiment 1)
The Actual Pressure from the dead weight applied on the piston
p= 4M+mg?d2……………………………..(1)The Standard Deviation of the samples obtained is represented
S=S2=(p1-p)2+(p2-p)2+…+(pi-p)2+…+(pn-p)2n-1……..(2)Gauge % Error that comes from the estimated and actual values
% error= estimated value-actual valueactual value*100%………………………….(3)Experiment 2)
Hydrostatic Thrust on the partly submerged surface
F=?gAh………………………(4)
Area=B*d=( horizontal distance)*(Vertical distance)d = depth of immersion for the submerged object
h – Depth of the centroid of the submerged area C, where
h=d-D2……………….…….(5) Thus giving the simplified equation for Hydrostatic Thrust on the submerged surface
F=?gBd22……………………(6)Moment of Thrust about pivot is given by
M=F*h”=W*L=m(applied mass)*g*lThe resolved equation giving the depth of line of action of thrust below the pivot
h”= 2mL?Bd2……………………..(7)The theoretical depth of center of pressure P below the free surface is specified by
h’=IxAh……………………..…..(8)The second moment of area of the immersed section about an axis in the free water surface is
Ix=IC+Ah……………..………(9)From the above equation you can then plug in values and obtain a equation with all known values
Ix= Bd312+Bd(d2)2=Bd33……(10)Depth below the pivot point will be
h”= h’+H-dUsing the above equation you can resolve to it to result in a theoretical result
h”=H-d3………………..………(11) Description of Experimental Setup
Equipment and Materials used are as follows:
Bourdon Tube pressure gage
Water
Piston Cylinder
The Armfield Hydrostatic Pressure Apparatus
Ruler
Ohaus Scout Scale
Procedure
Experiment 1:
For this experiment it was first required to make sure that the device was calibrated for accurate results. This was done by removing the piston and then filling up the cylinder with water. Then it was needed to tap the top the piston and get the air out. After that we started applying the known weights in increasing order while tapping it and rotating it every time to make sure that the air was out. For every weight the pressure was recorded from the gauge. This was also down in decreasing order and all values were recorded on the tables below.
Experiment 2:
For this experiment the apparatus needed to be level in all directions using the spirit level. After that it was then needed to locate the weight hangar in the groove at the end of the balance arm and make sure it is balanced. Then add a known weight on the end of the pivot arm and then balance the arm to maintain the depth of the submerged quadrant. This was repeated several time to obtain a broad range of values for different weights.
Data
Technical Data Activity 1
d = diameter of the piston = 17.84 mm
m = weight of the piston = 0.5 kg
Zero reading of the pressure gage = 28 kN ?mm2Range of the pressure gage 0°-270°Data for Activity 1: Bourdon Tube Pressure Gauge
Table SEQ Table * ARABIC 1: Increasing Mass Data for Activity 1
Increasing Pressure
Mass (kg) Actual Pressure (kN/M2) Gage Reading(kN/M2) Mean STD % error
Run 1 Run 2 Run 3 Run 4 Run 5 0.4536 37.424 41 40 41 41 41 40.8 0.447 9.021
0.9072 55.226 61 61 61 60 60 60.6 0.547 9.731
1.3608 73.040 79 80 79 78 79 79.0 0.707 8.160
1.8148 90.850 97 97 98 95 96 96.6 1.14 6.329
2.2685 108.65 113 113 113 112 113 112.8 0.447 3.820
Table SEQ Table * ARABIC 2: Decreasing Mass Data for Activity 1
Decreasing Pressure
Mass (kg) Actual Pressure (kN/M2) Gage Reading(kN/M2) Mean STD % error
Run 1 Run 2 Run 3 Run 4 Run 5 2.2685 108.65 113 113 113 112 113 112.8 0.447 3.820
1.8148 90.850 97 98 98 96 97 97.2 0.837 6.990
1.3608 73.040 79 79 79 78 80 79.0 0.447 8.160
0.9072 55.226 61 61 61 61 60 60.8 0.447 10.09
0.4536 37.424 42 44 43 41 41 42.2 1.30 12.76
Technical Data Activity 2
Length of Balance L = 280 mm
Quadrant to Pivot H = 200 mm
Height of Quadrant D = 100 mm
Width of Quadrant B = 75 mm
Data for Activity 2: Armfield Hydrostatic Pressure Apparatus
Table SEQ Table * ARABIC 3: Weight Increasing Activity 2 Data
Weight Increasing Mass (kg) d, (mm) h’, (mm) h”,(mm) F, (N)
Partly Submerged 0.05 46 -176.33 -22.33 -0.135
0.10 64 97.52 233.52 0.659
0.15 79 71.74 192.74 1.686
0.20 93 67.05 174.05 2.942
Fully Submerged 0.25 106 70.88 0.17 4.120
0.30 119 81.08 0 5.077
0.35 131 91.29 0 5.960
0.40 143 101.96 0 6.842
Table SEQ Table * ARABIC 4: Weight Decreasing Activity 2 Data
Weight Decreasing Mass (kg) d, (mm) h’, (mm) h”,(mm) F, (N)
Partly Submerged 0.20 96 66.78 170.78 3.249
0.15 81 70.55 189.55 1.847
0.10 65 93.89 228.89 0.717
0.05 45 -135.00 20.00 -0.166
Fully Submerged 0.40 143 101.96 0 6.842
0.35 132 92.16 0 6.033
0.30 120 81.90 0 5.150
0.25 108 72.37 0 4.267
Analysis of Data
Activity 1: Bourdon tube pressure gauge
Gauge Pressure vs. Actual Pressure (Increasing and Decreasing)
Figure SEQ Figure * ARABIC 1: Increasing and Decreasing Pressure for Gauge vs. Actual

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Gauge error vs. Actual Pressure
Figure SEQ Figure * ARABIC 2: Gauge Error vs. Actual Pressure (Increasing and Decreasing)

Standard Deviation vs. Actual Pressure
Figure SEQ Figure * ARABIC 3: Standard Deviation vs. Actual Pressure (Increasing and Decreasing)

Activity 2: Armfield Hydrostatic Pressure Apparatus
Thrust (N) vs. Depth of Immersion
Figure SEQ Figure * ARABIC 4: Activity 2: Thrust vs. Depth of Immersion

As the Depth of immersion increases so does the force as expected
Depth of Center of Pressure vs. Depth of Immersion
Figure SEQ Figure * ARABIC 5: Activity 2: Center of Pressure vs. Depth of Immersion

Discussion of Results
Looking at the Figures from Activity 1 it can be determine that there was some experimental error due to human interaction involved. Other reasons for the data to be skewed is because of the old equipment used that didn’t give very accurate readings. The spring behind the piston could have been wore which would allow the pressure to be skewed. For the gage reading we over estimated it compared to the actual pressure calculated. For Activity 2 the graphs for thrust vs. depth of immersion makes sense due to the laws of fluids. As the depth of immersion increases the force increases. Looking at the depth of immersion vs. depth of center of pressure gives little information to the experiment. I believe this is due to experimental error. This could have come from the fact that all measurements were observed by human eye and there is always error in that process.
Conclusions
The purpose of the experiment was to look at how buoyancy forces counteract and try to balance the thrust force from the top of surface of the fluid. Taking Bernoulli’s equation and looking at how the forces from they should balance themselves out by adding weights to increase the pressure. For the second experiment it was shown that using the water level and a known weight you could determine the center of pressure on a submerged object. The more the water was filled in the apparatus the more weight need to be applied to balance it out. This directly correlates to the fact that with increased immersion comes increased thrust force.
References
NCEES. (2016). FE Reference Handbook 9.4 Version. America: NCEES.

Appendix
Activity 1:

Activity 2:

General Notice
Abstract is 12 pt. Font Book Antiqua
The title is 18 pt. Arial
The name and course block is 12 pt. Arial
The rest of the lab report is 12 pt. Arial

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