es341 lab 2
TRANSCRIPT
ES-F341
F04
Lab 2
Title: Hydrostatic Forces on Vertical and Inclines Flat surfaces
Abdul Sayed, [email protected]
Ryan Johnson, [email protected]
Mi Chin Yi, [email protected]
Grant Cummings [email protected]
Cecilia Hull [email protected]
Date performed: 09/25/2014
Date due 10/2/2014
Introduction:
An engineer must take into account hydrostatic forces into structural design
considerations as they impose important forces on common structures such as dams, irrigation
canals, fluid storage tanks, and retaining walls.
Hydrostatic forces can be measured by calculating the pressure distribution on the objects
which is submerged. The main objective is to measure the hydrostatic forces exerted on vertical
and inclined flat surface. Pressure is defined as the force per unit area. Fluid density and fluid
depth are used to determine fluid pressure by Pressure = density x gravity x height.
Limitations in this experiment arise due to the water level not being stable after water
insertion. Angle measurement also created opportunity for error.
Equipment & Setup:
Equipment used in this experiment:
Center of Pressure apparatus (Model/Serial Number = 185269, type#1)
Angular Calibrator
Staff Guage
Metal weights
The illustration below details the equipment used in this experiment.
Above schematic of equipment used taken from:
Claydon, J. (2014). Centre of pressure. [online] Jfccivilengineer.com. Available at:
http://www.jfccivilengineer.com/centre_of_pressure.htm [Accessed 2 Oct. 2014].
Above is a picture of the equipment used, taken from:
Barve, N. (2014). Scitech Hydrostatic Force & Center of Pressure apparatus. [online]
Sci-tech.biz. Available at: http://www.sci-tech.biz/trainersDetail.php?Hydrostatic-Force-Center-
of-Pressure-apparatus-170 [Accessed 2 Oct. 2014].
Procedure:
1. Add water and using weights balance tank.
2. Add increments of water gradually and heften or lessen weights ever so slightly so
that observed angle may approach zero.
3. Make recordings of vertical height of water corresponding to a given load that zeroed
the angle.
4. Continue trial until a total of four data sets are obtained corresponding to heights
of water specified in Table 1.
5. Repeat the above steps but for an angle of 10 degrees.
Results:
Table 1 summarizes the collected measurements. Listed are the mass of the load arm [m],
and the vertical distance between the pivot and the water surface [h].
Table 2 and 3 contain the following data for angles of 0, and 10 degrees, respectively: the
mass of the load [m], the force of water against gate [FL], submerged height of gate [YG],
vertical distance to centroid of gate [hc], area of gate under water [AG], hydrostatic force on gate
[Fw], distance from water surface to center of pressure [Ycp] both theoretically calculated and
experimentally measured.
Data in lines 1-4 of tables are of “partial 1”; water level less than full, “partial 2”; water
level closer to full, “full” ; water level just reaches top of gate, and “above”; water level above
top of gate.
*Formatting for Table 2 and 3 taken from “Lab Handout 2” from Blackboard.
Table 1
Part A Part B
m (kg) h (m) m (kg) h (m)
Partial 1 0.050 0.154 0.050 0.152
Partial 2 0.100 0.132 0.100 0.130
Full 0.220 0.0990 0.220 0.0965
Above 0.400 0.0508 0.400 0.0495
Table 2 (θ = 0o)
m (kg)
FL (N)
YG
(m)hC
(m)AG
(m2)FW (N)
YCP,theor.
(m)YCP,exp (m)
0.050 .491 .154 .0770 .00978 7.39 .103 -.137
0.100 .981 .132 .0660 .00838 5.43 .0881 -.129
0.220 2.16 .0990 .0495 .00629 3.05 .0660 .0809
0.400 3.92 .0508 .0254 .00322 .804 .0339 1.18
Table 2 (θ = 10o)
m(kg)
FL (N)
YG
(m)hC
(m)AG
(m2)FW (N)
YCP,theor.
(m)YCP,exp (m)
0.050 .491 0.152 .0760 .00965 7.20 .101 -.137
0.100 .981 0.130 .0650 .00826 5.26 .0866 -.0854
0.220 2.16 0.0965 .0483 .00613 2.90 .0644 .0883
0.400 3.92 0.0495 .0246 .00314 .763 .0330 1.23
Discussion:
Figure 1: Plot of results from table 2 for Ycp theoretical vs mass and Ycp experimental vs mass
Figure 2: Plot of results from table 3 for Ycp theoretical vs mass and Ycp experimental vs mass
Questions:
1. Could this apparatus be used for other fluids to determine their center of pressure?
Yes, this apparatus can be used for any incompressible fluid.
2. What are the important forces to consider in your analysis?
The load from the metal weight, as well as the force from the hydrostatic pressure of water
were important forces to consider.
3. List sources of error.
Systematic error due to limitations of equipment, error arising from improperly interpreting
balance as being level, friction between moving parts were all sources of error.
4. Discuss your experimental and theoretical results
There is a considerable error in both experiments therefore, the results are not reliable.
In both cases, the curves do not match so theoretical and experimental data do not agree.
5. Would this experiment be suitable for two immiscible fluids? Explain.
Two fluids, despite if they do not mix, would be impractical to work with in this experiment
since that would add to the complexity of the procedure.
Conclusion:
Results from this experiment showed inverse correlation between theory and data. The
reason for this may be faulty data acquisitioning or erroneous processing.
According to the figures, we can see the results for both parts are not reliable based on the
difference between the theoretical value and the experimental value.
References:
Toniolo, H. (2014). [online] Classes.uaf.edu. Available at:
https://classes.uaf.edu/webapps/portal/frameset.jsp?tab_tab_group_id=_2_1&url=%2Fwebapps
%2Fblackboard%2Fexecute%2Flauncher%3Ftype%3DCourse%26id%3D_146492_1%26url
%3D [Accessed 2 Oct. 2014].
Claydon, J. (2014). Centre of pressure. [online] Jfccivilengineer.com. Available at:
http://www.jfccivilengineer.com/centre_of_pressure.htm [Accessed 2 Oct. 2014].
Barve, N. (2014). Scitech Hydrostatic Force & Center of Pressure apparatus. [online]
Sci-tech.biz. Available at: http://www.sci-tech.biz/trainersDetail.php?Hydrostatic-Force-Center-
of-Pressure-apparatus-170 [Accessed 2 Oct. 2014].
Appendix:
Observations:
G (height of gate) = 0.1016 meter
B (width of gate) = 0.0635 meter
R1 (distance from pivot to top of gate) = 0.1016 meter
R2 (distance from pivot to bottom of gate) = 0.2032 meter
RL (distance from pivot to weight) = 0.254 meter
*The following definitions and formulae taken from “Lab Handout 2” from Blackboard :
Definitions:
θ = angle of apparatus
RL = length of load arm (m)
R1 = radius to the upper edge (m)
R2 = radius to the lower edge (m)
B = width of gate (m)
G = height of gate (m)
W = specific weight of water (kN/m3)
m = mass on load arm (kg)
FL = force on load arm (N)
FW = resultant force of water against gate
(N)
h = vertical distance between the pivot
and the water surface (m)
hC = vertical distance from the water
surface to the centroid of the submerged
area of the gate (m)
AG = submerged area of the gate (m2)
Ycp = distance, along the angle of
incline, from the water surface to the
center of pressure (m)
Ψ = distance, along the angle of incline,
from the water surface to the centroid of
the submerged area of the gate (m)
YG= submerged height of the gate (m)
IO = second moment area of the
submerged area of the gate (m4)
Formulas:
Hc = YG/2
AG = B*YG
Here is a sample calculation for a mass of .05 kg for table 2
FL = mg = 0.05kg * 9.81m/s^2 = 0.491N
AG = B * YG = .0635m * .154m = 0.00978m^2
FW = γW*hC*AG = 9810N/m^3 * .077m * .00978m^2 = 7.39 kN
( [FLRL*cosθ] / Fw ) - h/cosθ = YCP, exp
( [.491*.254*cos(0)] / 7.39 ) - .154/cos(0) = -0.137
YCP, theor=Ψ+I0/(AG*Ψ)= Ψ+ B*YG3/12/(AG*Ψ)
=0.1+0.075*0.13/12/(0.00314*0.1)=0.029m