Water exerts a pressure on the bottom and sides of the vessel which holds it. Fill a vessel 1 cu. ft. in volume with water. If the water is weighed it is found to weigh about 62.5 lbs. Therefore 62.5 lbs. is pressing on the bottom of the box, the area of which is 144 sq. in. Therefore the pressure per square inch is 62.5 / 144 or .434 lb. The unit of pressure is the amount of pressure to the square inch. Pressure equals force per unit area.
A liquid also exerts pressure on the outside of any object immersed or pushed into it and the pressure increases with the depth. This phenomenon may be explained by considering a liquid as made up of a large number of thin horizontal layers, each layer supporting the weight of those above. The lower the layer, the greater the weight of liquid it has to support; hence the greater the pressure exerted upon it. This pressure has nothing to do with the size and shape of the vessel and is evenly exerted upon each square inch of surface.
The total pressure of a liquid upon any portion of the vertical sides of a vessel is equal to the weight of a column of the liquid, whose base and length are respectively the area of that portion of the side and its average depth. This may be explained in another way. The pressure against the vertical side of a tank at the surface of the water is zero, for the liquid has no depth. But the pressure on the side increases with the depth until we reach the bottom of the tank, when it is equal to the pressure against the bottom.
The average pressure on the side then is the pressure exerted on the middle of the side, and is equal to one-half the pressure per unit of surface against the bottom.
The following laws apply to liquids:
I. The pressure does not depend upon the size or shape of the vessel. The pressure increases with the vertical depth below the free surface.
II. At any point in a liquid, the upward, downward, and lateral or sideways pressures are equal.
III. To find the lateral pressure of water, upon the sides of a tank, multiply the area of the submerged portion of the side in inches, by the pressure of one-half the depth.
As an example: What is the lateral pressure on one side of a tank 20 in. wide and 2 ft. deep (notice how there is not a reference to volume?)
20 in. X 24 in. = 480 sq. in., area of side.
2 ft. X .434 = .868 lb., pressure at bottom of tank.
.868 / 2 = 434 lb., average pressure due to one-half the depth of tank.
.434 X 480 = 208.32 lbs., pressure on one side of the tank.
This can be found at: http://chestofbooks.com/crafts/metal/Applied-Science-Metal-Workers/69-Water-Pressure.html
Thus for aquariums we build that are NOT all glass AND are framed (ie braced with wood) the safety factor CAN be reduced. For enclosures that are all glass or not framed, the following should help clear up the mystery behind the safety factor calculations.
More information on this can be found at: http://www.fnzas.org.nz/index.php?PG=glass1
As well as a downloadable excel version of the formula that follows.
NOTE: The calculations only consider the water to the top edge of the glass. If the glass is a window below the surface then it is outside the scope of this article.
Calculations
Terms Used:
Length in mm (L): The length of the aquarium.
Width in mm (W): The width of the aquarium from front to back.
Height in mm (H): The overall depth of water that is in contact with the glass, but does not exceed its upper edge.
Thickness in mm (t): The thickness of the Glass.
Water Pressure (p): The force in Newton's (N).
Allowed Bending Stress (B): Tensile Strength / Safety Factor
Modulus of Elasticity (E): Elastic Strength
The length to height ratio effects the strength of the glass. The table below lists alpha and beta constants to be used based on with the length to height ratio.
Table of Alpha and Beta Constants used in the Calculations
For Side Panels For Bottom Panels
Ratio of L/H Alpha Beta Alpha Beta
0.5 0.003 0.085
0.666 0.0085 0.1156
1.0 0.022 0.16 0.077 0.453
1.5 0.042 0.26 0.0906 0.5172
2.0 0.056 0.32 0.1017 0.5688
2.5 0.063 0.35 0.111 0.6102
3.0 0.067 0.37 0.1335 0.7134
When the ratio is less than 0.5, use Alpha and Beta values for 0.5.
When the ration is greater than 3, use Alpha and Beta values for 3.
Note: For bottom panel, use Length to Width ration (L/W).
The water pressure (p) is directly proportional to the Height (H) x the force of gravity (approx 10 (9.81 for people who want to be exact)).
p = H x 10 in N/mm2
The bending stress allowed (B) is equal to the Tensile Strength of glass / safety factor.
B = 19.2 / 3.8 = 5.05N/mm2 (Safety factor = 3.8)
Calculations for Front and Side Glass Panels:
The thickness of the glass (t) is proportional to the (square root of width factor (beta) x height (H) cubed x 0.00001 / allowable bending stress (B)).
so; t = SQR (beta x H3 x 0.00001 / 5.05) in mm.
Select beta and alpha from the previous chart based on the length to height ratio.
The deflection of the glass is proportional to
(alpha x water pressure (p) x 0.000001 x Height4)
(Modulus of elasticity (E) x Thickness (t) cubed).
Deflection =
(Alpha x p x 0.000001 x H4) / (69000 x t3) in mm.
Example: (Warren's new tank)
Aquarium Length = 3000mm
Aquarium Height = 950mm
Safety Factor = 3.8 L/H >3 therefore Beta = 0.37 and Alpha = 0.067
p = 950 x 10 = 9500N/m2
Side Thickness:
t = SQR (0.37 x 0.9503 x 0.00001 / 5.05)
= 25.06mm
Deflection = (0.067 x 9500 x 0.000001 x 9504) / (69000 x 253)
= 0.48mm
Calculations for Bottom Glass Panel:
There is a small difference when calculating the bottom panel thickness. Beta is now calculated from the Length/Width (where the length L is the larger dimension - therefore L/W is always >=1). The Height is still used to calculate the pressure. Be sure to use the Bottom Panel Alpha/Beta values.
The thickness of the bottom glass (t) is proportional to the square root of width factor (beta) x height (H) cubed x 105 / allowable bending stress (B), - the same as the side panels.
t = SQR (beta x H3 x 0.00001 / 5.05) in mm
Select beta and alpha from the previous chart based on the length to width ratio.
The deflection of the glass is proportional to (alpha x water pressure (p) x 10-6 x Height4) / (Modulus of elasticity (E) x Thickness (t)cubed).
Deflection = (Alpha x p x 0.000001 x H4) / (69000 x t3) in mm.
Example: (Warren's new tank)
Aquarium Length = 3000mm
Aquarium Width = 900mm
Aquarium Height = 950mm
Safety Factor = 3.8 L/W >3 therefore Beta = 0.7134 and Alpha = 0.1335
p = 950 x 10 = 9500N/m2
Bottom Thickness:
t = (SQR (0.7134 x 9503 x 0.00001) / 5.05)
= 34.8mm
Deflection = (0.1335 x 9500 x 0.000001 x 9504) / (69000 x 34.833)
= 0.355mm
A liquid also exerts pressure on the outside of any object immersed or pushed into it and the pressure increases with the depth. This phenomenon may be explained by considering a liquid as made up of a large number of thin horizontal layers, each layer supporting the weight of those above. The lower the layer, the greater the weight of liquid it has to support; hence the greater the pressure exerted upon it. This pressure has nothing to do with the size and shape of the vessel and is evenly exerted upon each square inch of surface.
The total pressure of a liquid upon any portion of the vertical sides of a vessel is equal to the weight of a column of the liquid, whose base and length are respectively the area of that portion of the side and its average depth. This may be explained in another way. The pressure against the vertical side of a tank at the surface of the water is zero, for the liquid has no depth. But the pressure on the side increases with the depth until we reach the bottom of the tank, when it is equal to the pressure against the bottom.
The average pressure on the side then is the pressure exerted on the middle of the side, and is equal to one-half the pressure per unit of surface against the bottom.
The following laws apply to liquids:
I. The pressure does not depend upon the size or shape of the vessel. The pressure increases with the vertical depth below the free surface.
II. At any point in a liquid, the upward, downward, and lateral or sideways pressures are equal.
III. To find the lateral pressure of water, upon the sides of a tank, multiply the area of the submerged portion of the side in inches, by the pressure of one-half the depth.
As an example: What is the lateral pressure on one side of a tank 20 in. wide and 2 ft. deep (notice how there is not a reference to volume?)
20 in. X 24 in. = 480 sq. in., area of side.
2 ft. X .434 = .868 lb., pressure at bottom of tank.
.868 / 2 = 434 lb., average pressure due to one-half the depth of tank.
.434 X 480 = 208.32 lbs., pressure on one side of the tank.
This can be found at: http://chestofbooks.com/crafts/metal/Applied-Science-Metal-Workers/69-Water-Pressure.html
Thus for aquariums we build that are NOT all glass AND are framed (ie braced with wood) the safety factor CAN be reduced. For enclosures that are all glass or not framed, the following should help clear up the mystery behind the safety factor calculations.
More information on this can be found at: http://www.fnzas.org.nz/index.php?PG=glass1
As well as a downloadable excel version of the formula that follows.
NOTE: The calculations only consider the water to the top edge of the glass. If the glass is a window below the surface then it is outside the scope of this article.
Calculations
Terms Used:
Length in mm (L): The length of the aquarium.
Width in mm (W): The width of the aquarium from front to back.
Height in mm (H): The overall depth of water that is in contact with the glass, but does not exceed its upper edge.
Thickness in mm (t): The thickness of the Glass.
Water Pressure (p): The force in Newton's (N).
Allowed Bending Stress (B): Tensile Strength / Safety Factor
Modulus of Elasticity (E): Elastic Strength
The length to height ratio effects the strength of the glass. The table below lists alpha and beta constants to be used based on with the length to height ratio.
Table of Alpha and Beta Constants used in the Calculations
For Side Panels For Bottom Panels
Ratio of L/H Alpha Beta Alpha Beta
0.5 0.003 0.085
0.666 0.0085 0.1156
1.0 0.022 0.16 0.077 0.453
1.5 0.042 0.26 0.0906 0.5172
2.0 0.056 0.32 0.1017 0.5688
2.5 0.063 0.35 0.111 0.6102
3.0 0.067 0.37 0.1335 0.7134
When the ratio is less than 0.5, use Alpha and Beta values for 0.5.
When the ration is greater than 3, use Alpha and Beta values for 3.
Note: For bottom panel, use Length to Width ration (L/W).
The water pressure (p) is directly proportional to the Height (H) x the force of gravity (approx 10 (9.81 for people who want to be exact)).
p = H x 10 in N/mm2
The bending stress allowed (B) is equal to the Tensile Strength of glass / safety factor.
B = 19.2 / 3.8 = 5.05N/mm2 (Safety factor = 3.8)
Calculations for Front and Side Glass Panels:
The thickness of the glass (t) is proportional to the (square root of width factor (beta) x height (H) cubed x 0.00001 / allowable bending stress (B)).
so; t = SQR (beta x H3 x 0.00001 / 5.05) in mm.
Select beta and alpha from the previous chart based on the length to height ratio.
The deflection of the glass is proportional to
(alpha x water pressure (p) x 0.000001 x Height4)
(Modulus of elasticity (E) x Thickness (t) cubed).
Deflection =
(Alpha x p x 0.000001 x H4) / (69000 x t3) in mm.
Example: (Warren's new tank)
Aquarium Length = 3000mm
Aquarium Height = 950mm
Safety Factor = 3.8 L/H >3 therefore Beta = 0.37 and Alpha = 0.067
p = 950 x 10 = 9500N/m2
Side Thickness:
t = SQR (0.37 x 0.9503 x 0.00001 / 5.05)
= 25.06mm
Deflection = (0.067 x 9500 x 0.000001 x 9504) / (69000 x 253)
= 0.48mm
Calculations for Bottom Glass Panel:
There is a small difference when calculating the bottom panel thickness. Beta is now calculated from the Length/Width (where the length L is the larger dimension - therefore L/W is always >=1). The Height is still used to calculate the pressure. Be sure to use the Bottom Panel Alpha/Beta values.
The thickness of the bottom glass (t) is proportional to the square root of width factor (beta) x height (H) cubed x 105 / allowable bending stress (B), - the same as the side panels.
t = SQR (beta x H3 x 0.00001 / 5.05) in mm
Select beta and alpha from the previous chart based on the length to width ratio.
The deflection of the glass is proportional to (alpha x water pressure (p) x 10-6 x Height4) / (Modulus of elasticity (E) x Thickness (t)cubed).
Deflection = (Alpha x p x 0.000001 x H4) / (69000 x t3) in mm.
Example: (Warren's new tank)
Aquarium Length = 3000mm
Aquarium Width = 900mm
Aquarium Height = 950mm
Safety Factor = 3.8 L/W >3 therefore Beta = 0.7134 and Alpha = 0.1335
p = 950 x 10 = 9500N/m2
Bottom Thickness:
t = (SQR (0.7134 x 9503 x 0.00001) / 5.05)
= 34.8mm
Deflection = (0.1335 x 9500 x 0.000001 x 9504) / (69000 x 34.833)
= 0.355mm
