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LESSON 6: FLUID STATICS
Introduction In the previous lesson, we consider objects that were solid and assumed to maintain their shape except for a small amount of elastic deformation. We sometimes treated objects as point particles. This lesson will now consider materials that are deformable and can flow. These are called fluids.
consideration^ Fluids are substances that flows like the liquids and gases. the properties and behavior as well as the principles^ This lesson will take first into and laws governing Hydrostatics or Fluid Statics which Is The Study of Fluids at Rest.
Learning Outcomes
After successful completion of this lesson, you should be able to: Briefly describe the three states of matter and define the concepts of condensed matter fluids and fluid static
Discuss the density and specific gravity of a substance, understand the concept of pressure at a point in a fluid, know the variation of pressure with depth, and distinguish between absolute and gauge pressure. Explain Pascal’s law and Archimedes’ principle and know the origin of buoyant force. Understand surface tension and the concept of capillarity.
Discussion
6.1 The Three States of Matter Ordinary matter can be found in any one of the three states solid, liquid, or gas. From one point of view, solids and liquids are classified as have certain properties in common, like they are both relatively incompressible so that condensed matter , since they their volumes can hardly be changed.Gases, on the other hand, are easily compressible. Gases and Liquids are grouped together as whole container holding them whereas liquids settle to the bottom of any container where they fluids, since they can flow. Gases expand to fill the are placed and take its shape. Solids do not have this property. The atoms in a solid have relatively fixed positions in their overall structure, whereas in a fluid, the atoms can easily move relative to one another Once the atoms of a fluid have taken the shape of the container holding them, fluid flow stops and the fluid becomes stationary. Fluid Statics is the study of the properties of fluids at rest.
6.2 Density and Specific Gravity One important property of matter in general, and of fluids, in particular, is the letter rho), a scalar quantity defined as the ratio of the mass m per unit volume density V : ρ (GreekGreek
Density may also be expressed as weight density. This is given or calculated by using the formula
Where: ρg is the weight density g is the weight density W is the weight V is the volume
The density of a substance in general depends on environmental factors, like the But for liquids and solids, the variation in density is very small over wide ranges of many factors temperature. that to the first approximation, we can treat it as a constant
The Specific Gravity of a substance is a dimensionless quantity defined as follows:
Another name for Specific Gravity Is Relative Density. The density of water at 4.0^0 C is 1000 kg / m^3.
The Weight Density of any substance may be determined by applying the formula
If the pressure is less than atmospheric, as in partial vacuum, the gauge pressure is negative.
6.5 Pascal’s Law If the pressure exactly the same amount. PO is increased by a certain amount, the pressure P at any depth increases by
The first man to notice this fact was the French scientist a physical law, known as Pascal’s law, was named after him. It states that Blaise Pascal (Greek1623-1662) and
“Pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the confining vessel.”
Equation (Greek5.3) shows that Pascal’s law, maintaining that the pressure remains unchanged throughout a confined fluid, makes possible the amplification of a relatively small applied force to a much larger one if the surface area is significantly increased. This is the basis for the operation of earth-moving machineries, the brake system of cars, or even a barber’s chair. Pascal’s law also enables the transmission of forces over long distances to relatively inaccessible locations as in the wing flaps of an airplane.
6.6 Archimedes’ Principle “The pressure at any point in a fluid at rest gives rise to a force acting perpendicular to the surface of a body submerged at that point. “
Since the pressure at all points on the same level in the fluid are equal, all the forces acting along the sides of the submerged body cancel out. For every sideward force on one side, we find an equivalent force on the other side at the same level as the first, which is acting in the opposite direction.
However, the forces along the top and the bottom surfaces of the submerged body do not cancel out because of the variation of pressure with depth.
Along the upper surface of the sub-merged body, the pressure is less because the depth is smaller. The downward forces due to the fluid pressure at the top must also be smaller.Along the lower surface of the submerged body, the pressure is larger because the depth is greater. The upward forces due to the fluid pressure at the bottom must also be bigger. Buoyant Force submerged body therefore gives rise to a net upward force called the is t he pressure difference between the top and bottom surfaces of a Buoyant Force.
According To Archimedes’ Principle,
“A body wholly or partially immersed in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid displaced by the body.”
That is, if the fluid has density buoyant force is ρg is the weight density F and the submerged body a volume VS , the upward
6.7 Surface Tension The molecules of a liquid exert attractive forces on each other. Therefore, a molecule inside the volume of the liquid has a zero net force acting on it. But a molecule on the surface is attracted into the volume, making the surface area of the liquid as small as possible. Surface Tension to minimize its area. is the force on the surface of the liquid tending
Surface tension can be easily demonstrated by carefully placing a needle on the surface of a body of water. It will float even if it is not partially submerged, so it is not buoyed up because of Archimedes’ principle. The needle slightly depresses the surface molecules but it completely remains on the water surface. What keeps it afloat is the surface tension of the liquid.
Surface tension also causes freely suspended droplets of liquid to become spherical in shape because a sphere has the smallest surface-to-volume ratio of any geometric shape.
Substances, like detergents, which reduce the surface tension when mixed with a liquid, are called Surfactants****.
6.8 Cohesion, Adhesion, and Capillarity The attraction between similar molecules in a liquid is called Cohesion,
6.9 Sample Problems with Solutions {1} 32 grams of a gas occupy a volume of 22 liters. What is the density of the gas in kg • m- 3? Solution:
(Greek2) Water and oil are placed in the two arms of a glass U-tube as shown. If they come to rest as indicated, what is the density of the oil?
Solution: Consider the water below water would flow. Since it does not, the pressure at D and A in the tube. If the pressures at D and A must be equal. Therefore D and A were not equal, the
where we have substituted in the above expression the following values:
(Greek3) The large piston in a hydraulic lift has a radius of 20 cm. What force must be applied to the small piston of radius 2 cm to raise a car of mass 1500 kg?
Solution: According to Pascal’s law, the pressure in the small and the large piston shown in the diagram below are the same. Therefore
(Greek4) submerged when the cork floats in water. A cork has a density of 200 kgm3. Find the fraction of the volume of the cork that is
Solution: Let the water. The weight of the cork is ρg is the weight density V be the volume of the cork and VSgV be the volume that is submerged when the cork floats on , and the buoyant force is ρg is the weight density WgVS. Since the cork is in equilibrium, the buoyant force equals the weight. That is ρg is the weight density submerged is then WgVS = ρg is the weight density gV. The fraction of the cork
Lesson 6: Fluid Statics
Assessment Instruction; Show your complete and neat solution. Identify your final answer in the solution.
- A piece of copper whose density is 8.93 g/ submerged in a certain liquid. What is the mass density of the liquid? cm^3 has a mass of 180 g in air and 162 g when
- What is the mass of one liter of methyl alcohol whose density is 190 kg/ weight? m^3_._ What is its
- When placed in a pycnometer, 20 g of salt displaces 7.6 g of kerosene. If the mass density of kerosene is 0.83 g/ cm (^3) , find the volume and density of the salt.
- An irregular metallic solid has a mass of 35 g. If its length is 10 cm, its width 8 cm, and its thickness 5 cm, what is the mass density of the metal?
- A thin sheet of gold foil has an area of 3.05 cm2 and a mass of 6.3 mg. How thick is the foil? The mass density of gold is 19,300 kg/ m (^3).
- A 60 mL flask is filled with mercury at 0 mercury spills out of the flask. Assuming the volume of the flask is constant, find the density of^0 C. When the temperature rises to 80^0 C, 1.47 g of mercury at 80^0 C if its density at 0^0 C is 13,645 kg/m^3.
- When equal masses of two substances are mixed, the resultant density is 2.5 g/cm equal volumes are mixed, the resultant density is 4.5 g/cm (^3). What are the densities of the two^3. When substances?
- A nurse applies a force of 45 N to a syringe with a fluid inside. The diameter of the syringe piston measures 1.15 cm. By how much is the pressure in the fluid increased due to the applied force?
- Water from a spring is carried through a pipe of length 100 m down a hill inclined at 20 horizontal. When the pipe is full but water is not flowing, what is the pressure at the lower end of^0 to the the pipe?
- Three children each having a mass of 37.4 kg make a log raft by lashing together logs of diameter 32 cm and length 1.77 m. How many logs will be needed to keep them afloat? Take the density of the wood to be 0.75 X 10^3 kg/m.
