ER1432 Civil Engineering Hydraulics and MaterialsSolution.pdf
ER1432 Civil Engineering Hydraulics and Materials
Purpose: Demonstrate Archimedes’ principle of buoyancy
Background: Buoyant force is the weight equivalent of the volume of displaced fluid
Any floating object displaces its own weight of fluid.
— Archimedes of Syracuse
"The works of Archimedes." p. 257. Retrieved 11 March 2010. Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced. https://en.wikipedia.org/wiki/Archimedes%27_principle
We have the above apparatus in the lab to determine the weight of an object in water, however, we will be not be using it.
Place a known weight in a cardboard “boat” and predict the location of the water line. Some sticky tape may be needed on the boat as a waterproofing measure.
Since density and hence specific weight of a fluid are affected by temperature, students must take a temperature reading of the water and consult a fluid properties table in a textbook for the value of density, ρ, or specific weight, γ, of water.
Students must ensure by calculation that their boat will indeed float with the provided weight.
Students will mark on the boat where they expect the waterline to be prior to placing the boat in the water.
Working equation: For a floating body, the buoyant force is the specific weight of the water multiplied by the volume of displaced water or
Fb = γ (volume displaced) = ρg (volume displaced) = ρg (A) (z) where z is the submerged depth which must be solved for in the equation.
A is the base area of the rectangular boat and z is your predicted depth of submergence.
Students should see that weight-to-displaced volume ratio must be less than the specific weight of water for the vessel to float. Alternately, if the weight of the vessel divided by the displaced volume of water > ρg then we can expect the boat to sink.
Typically, the weight of the boat itself is negligible compared to the weight of the object placed in the boat because the boat is made of cardboard or poster board for this experiment. Clearly, we cannot neglect the weight of a boat or ship in real life.
In any event, the total weight may be used for this experiment and the above equation can be rewritten as: z = (weight of object + weight of boat itself)/ γwA or
z = Weighttotal/γwA = mg/ρgA = m/ρA
Question: (to be answered as part of your lab write-up): If just one type of object or substance is placed in the boat, how can the specific gravity of this particular object or substance be determined? Explain your procedure and show by calculation in your lab write-up.
Do not forget to report the temperature of the water and other pertinent measurements in your lab report.
Reference: Fb = weight of displaced fluid = [weight of object in air – weight of object in water]
Specific weight of water = (density of water) (acceleration of gravity) or γ = ρg N/m3 = kg-(m/s2)/m3
F = ma or W = mg
Specific gravity of a substance = ρsubstance/ρwater at std. conds. = γsubstance/γwater at std. conds.
Specific gravity of object = [weight of object/ weight of equivalent volume of water]
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