Fluid Properties Density and Surface Tension

Topics: Density, Force, Fundamental physics concepts Pages: 8 (2132 words) Published: February 11, 2012
Expirement 1
Fluid Properties: Density and Surface Tension

Table of Contents:

The object of this experiment was to determine the density of a fluid by performing three different methods and use that determined density to calculate the surface tension of the fluid.

The density of any substance is defined as the mass per unit volume and is denoted by ρ.
ρ = m / V (1)
m is the mass of a substance and V is the volume occupied by the mass. The density of a liquid remains sensibly constant because the volume occupied by a given mass of a liquid is almost invariable. From this it may be noted that a liquid may be taken as virtually incompressible. There are several different methods that can be used to determine a fluid’s density. One method is to weigh a known volume of the liquid using a graduated cylinder or beaker and a scale. The beaker is weighed empty and then filled to a certain volume according to the graduations on it and weighed again. The difference in weight divided by the volume gives the weight per unit volume of the liquid. This measurement is expressed as,

ρ = (m2 – m1) / V(2)
where m1 is the weight of the empty beaker and m2 is the weight of the filled beaker.
A second method of finding density involves measuring the buoyant force exerted on a submerged object. The difference between the weight of an object in air and the weight of the object in liquid is known as the buoyant force. The buoyant force B is found as

B = W1 – W2(3)
where W1 is the weight of the object in air and W2 is the weight of the submerged object. The buoyant force is equal to the difference between the weight of the object in air and the weight of the object while submerged. Dividing this difference by the volume displaced, V, gives the weight per unit volume from which density can be calculated.

ρ = B / V (4)
A third method of making a density measurement involves the use of a calibrated hydrometer cylinder. The cylinder is submerged in the liquid and the density is read directly on the calibrated portion of the cylinder itself. A hydrometer is an instrument used to measure the specific gravity of a fluid, usually with a reference to pure water at room temperature. This means that the specific gravity of a fluid is the ratio of the mass of a liquid to the mass of an equal volume of pure water. To calculate the density of a fluid with this instrument, suspend the hydrometer bulb end down in a cylinder filled with fluid and wait for it to come to rest. It is important that the hydrometer does not touch the sides of the cylinder so that the fluid’s other properties do not interfere with the reading. On the length of the hydrometer there are calibration marks. The value that is at the meniscus of the fluid is the specific gravity of the fluid. It should be recorded and is denoted as s. To calculate the density from this value, multiply the hydrometer reading by the known density of water.

ρ = s * ρwater (5)
Another important fluid property is surface tension and is defined as the energy required to pull molecules of liquid from beneath the surface to the surface to form a new area. In a liquid away from the liquid surface, the molecules have random orientations and cause an attraction on each other that is equal in all directions. However, the molecules are rearranged when a liquid surface is formed. The resulting unbalanced attraction of the molecules on each other causes the liquid surface to behave as if the surface were a stretched membrane. The tension in this hypothetical membrane, expressed as a force per unit length [F/L] and given the symbol σ, is the surface tension of the liquid. The magnitude of the surface tension depends on the temperature and the second fluid (gas or liquid) in contact with the surface. A surface tension meter is used to measure this...

Bibliography: Introduction to Fluid Mechanics, 3rd Edition
William S. Janna (1993)
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