Chapter 7: Solid and Fluids

Objectives Describe the properties of solids, liquids, and gases. Calculate tensile stresses and strains. Calculate the pressure at a point in static fluids. Apply Archimedes’ principle of buoyancy. Apply Bernoulli’s principle and the equation of continuity to solve practical problems in fluid flow.

Solids, Liquids, and Gases Matter exists in the following three recognizable states: Solid: Has a definite shape and volume Liquid: Has a definite volume but no definite shape Gas: Has no definite shape and no definite volume

Interatomic Forces Definition: The forces exerted by atoms on one another that help to determine the structure and behavior of solids, liquids, and gases. Example: The interatomic force in a solid can be thought of as being exerted by elastic springs, as shown in the following figure:

Stress Definition: The force per unit area acting on the body. Unit: The unit is N/m2, which is also called the pascal. Types: The following are the three types of stresses: Tensile: A normal force that tends to elongate the object. This force creates tension in the material. Shear: A force acting parallel to the face of an object, which deforms the body in the form of a “sliding” or “twisting” change in its shape.

Stress (cont.) Hydraulic: A uniform pressure applied on an object from all sides, in general, exerted by liquids. The following figure describes all three types of stresses.

Strain Definition: The fractional change in the dimensions of the body. Formula: It is given by the relation: Stress = modulus of elasticity * strain Types: Normal strain: If a body elongates or shortens by a length, l, from its original length, L, the normal strain of the body is defined as the fractional increase or decrease in length, given by Normal strain =

Strain (cont.) Tensile Strain: If the stress is tensile, the body elongates, l is positive, and the normal strain is positive. where F is the force applied, A is the cross-sectional area, and E is the modulus of elasticity, called Young’s modulus.

Stress-Strain Curve The stress–strain curve in the following figure, shows a linear relationship between stress and strain up to the proportional limit .

Young’s Modulus The following table lists the yield strength, the ultimate strength, and Young’s modulus of few common materials

Properties of Static Fluids The properties useful for describing a static fluid at a point are: Density: Definition: Mass of a given volume of the substance divided by its volume, given by Unit: The SI unit is kg/m3, often expressed in g/cm3.

Properties of Static Fluids (cont.) The following table lists the densities of some common substances in g/cm3.

Properties of Static Fluids (cont.) Pressure: Definition: Force exerted by a fluid at a point divided by the area of the surface, given by Unit: The SI unit is N/m2, given the name pascal. The following figure depicts the calculation of pressure in the case of a small vertical cylinder filled with a fluid and with its base at the point.

Measurement of Atmospheric Pressure The atmospheric pressure at any point can be measured using a simple device called a mercury barometer that works on the basis of p = h g where, p is the pressure, h is the depth of the fluid, is the density of the fluid, and g is the acceleration due to gravity. The following figure depicts a mercury barometer.

Pascal’s Principle Statement: When pressure is applied to an enclosed static fluid, the pressure is transmitted undiminished to every part of the fluid. Example: A device called the hydraulic press or lever works on Pascal’s principle, as shown in the following figure:

Ideal Fluids An ideal fluid is a fluid that has the following properties: No viscosity Incompressible Laminar flow

Bernoulli’s Principle Statement: There is a simple relationship between the pressure, height, and velocity of flow. The following figure depicts Bernoulli’s equation, which is given by

Application of Bernoulli’s Principle The following are the areas where Bernoulli’s principle is applied: Airplane Wing: The following figure describes the application of Bernoulli’s principle. The lift on the wing can be explained using the principle.

Application of Bernoulli’s Principle (cont.) Venturi Meter: A venturi meter is a device for measuring the speed with which a fluid is flowing in a pipe, as shown in the following figure. The pressure difference at the inlet and the narrow end is calculated using Bernoulli’s Principle.

Application of Bernoulli’s Principle (cont.) Pitot Tube: An arrangement called the Pitot tube helps find the airspeed of an airplane applying Bernoulli’s equation between the stagnant point and the point where the air stream is in full flow, as in the following figure:

Summary Solids are characterized by a definite shape, but fluids take the shape of their containing vessel. Crystalline solids have a regular three- dimensional arrangement of their atoms, and the atoms exert forces on one another. Interatomic forces are less in liquids than in solids. The stress on a solid is defined as the force applied per unit area. Most solids, such as steel and aluminum, exhibit the property of elasticity.

Summary (cont.) The density of a substance is the mass of a certain volume of the substance divided by the volume. Pressure is force divided by area. The pressure in a static fluid depends only on the depth of the point below the free surface and is given by h  g. A mercury barometer helps find the atmospheric pressure. Gauge pressure is the difference between the absolute pressure at a point and the atmospheric pressure.

Summary (cont.) Pascal’s principle states that a pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid. Archimedes’ principle states that when a body is immersed in a fluid, it experiences an upward force equal to the weight of fluid that it displaces. An ideal fluid has no viscosity, is incompressible, and exhibits orderly laminar flow without any turbulence. Bernoulli’s equation, which is derived from the law of conservation of energy, is: P +  g h + (½)  v2 = constant.