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FLUIDS MOTION for production engineering

Fluid statics studies the behavior of stationary fluids, including pressure and forces exerted by liquids in various engineering applications. Key concepts include absolute pressure, gauge pressure, hydrostatic pressure, and buoyant force as described by Archimedes' principle. Practical applications include hydraulic systems and buoyancy effects in everyday situations like hot air balloons and ships.

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FLUID MOTION
Fluid statics is a field of fluid mechanics that studies the behaviour of fluids when they are at rest. It includes investigating the pressure fluids exert and the forces they experience when not moving. Fluid statics is an important field of study with numerous applications in various fields such as hydraulic systems, civil engineering, aerospace engineering, biomedical engineering, environmental engineering, and marine engineering. It is used to design and analyze systems that involve the transmission of force and energy using fluid power, as well as to study the movement of fluids in the environment and blood flow in the human body.
Pressure Pressure is defined as the force per unit area applied to an object. Fluid pressure is a measure of the intensity of the force applied to an object, and it is typically expressed in units of force per unit area, such as pascals (Pa) or pounds per square inch (psi). In fluid mechanics, pressure is an important concept used to analyze fluids’ behavior and the forces they exert on objects. Pressure can be defined as external normal force per unit area; its SI unit is N/m2 or Pascal (Pa). Pressure = Normal Force/Area
(a) A person being poked with a finger might be irritated, but the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is enough to break the skin.
Absolute pressure: This is the pressure of a fluid relative to a perfect vacuum. It is the sum of the gauge pressure and atmospheric pressure. Gauge pressure: This is the pressure of a fluid relative to atmospheric pressure. It measures the fluid pressure in a system that is open to the atmosphere. Vapor pressure: This is the pressure exerted by a vapor in equilibrium with its liquid phase. It is an important concept in thermodynamics and is used to determine the boiling point of a liquid. Hydrostatic pressure: This is the pressure exerted by a fluid at rest. It is related to the density of the fluid, the gravitational acceleration, and the height of the fluid above a reference point. Differential pressure: It is the difference in pressure between two points in a system. It is used to measure the pressure drop across a device or system. Static pressure: This is fluid pressure at rest in a system. It calculates the forces exerted by a fluid on an object in a static fluid. Dynamic pressure: This is the pressure of a fluid in motion. It calculates the forces exerted by a fluid on an object in a moving fluid. Types of Pressure
(a) Atoms in a solid are always in close contact with neighboring atoms, held in place by forces represented here by springs. (b) Atoms in a liquid are also in close contact but can slide over one another. Forces between the atoms strongly resist attempts to compress the atoms. (c) Atoms in a gas move about freely and are separated by large distances. A gas must be held in a closed container to prevent it from expanding freely and escaping.
What is Hydrostatic Pressure? Hydrostatic pressure is defined as“The pressure exerted by a fluid at equilibrium at any point of time due to the force of gravity”. p = ρgh hydrostatic pressure: where, p -is the pressure exerted by the liquid in N.m-2 or Pa ρ- is the density of the liquid in kg.m-3 g- is the acceleration due to gravity taken as 9.81m.s-2 h -is the height of the fluid column in m
The volume of real fluids changes when they are expanded or compressed by an external force or the change of pressure or temperature. The property of volume change is called compressibility and a fluid whose volume changes is called compressible fluid. On the other hand, an incompressible fluid is a fluid which is not compressed or expanded, and its volume is always constant. In reality, a rigorous incompressible fluid does not exist.
The magnitude of compressibility effect can be judged with flow velocity. For air, when flow velocity is 100 m/s or less, the air is treated as an incompressible fluid, and when the velocity is greater than 100 m/s, the air is treated as compressible fluid. As shown in Figure 3.19, an air flow with low velocity like breeze is an incompressible fluid while an air with high velocity like a flow around an airplane is a compressible fluid. An incompressible fluid without viscosity is called an ideal fluid or a perfect fluid. An ideal fluid really does not exist. However, because an ideal fluid is easy to handle theoretically, it plays an important role for the basics of fluid dynamics.
Forces on a fluid element in hydrostatic equilibrium - Pressure in fluids
The external static pressure applied on a confined liquid is distributed or transmitted evenly throughout the liquid in all directions
Pascal’s principle examples in real life Pascal’s law finds numerous examples in our daily life such as : automobiles hydraulic brake system hydraulic jack hydraulic press hydraulic machines.
Two pistons of a hydraulic lift have diameters of 60 cm and 5 cm. What is the force exerted by the larger piston when 50 N is placed on the smaller piston?
Solution Since, the diameter of the pistons are given, we can calculate the radius of the piston This means, with the force of 50 N, the force of 7200 N can be lifted.
A hydraulic system is used to lift a 2000-kg vehicle in an auto garage. If the vehicle sits on a piston of area 0.5 square meter, and a force is applied to a piston of area 0.03 square meters, what is the minimum force that must be applied to lift the vehicle?
A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 m2 . If the chair is attached to a piston of area 0.1 m2 , how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg.
The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid Archimedes’ Principle
What Is a Buoyant Force? The buoyant force is the upward force exerted on an object wholly or partly immersed in a fluid. This upward force is also called Up thrust. Due to the buoyant force, a body submerged partially or fully in a fluid appears to lose its weight, i.e. appears to be lighter. The following factors affect buoyant force: •the density of the fluid •the volume of the fluid displaced •the local acceleration due to gravity BUOYANT FORCE The buoyant force is the net upward force on any object in any fluid.
Archimedes’ Principle Equation Archimedes’ principle tells us that this loss of weight is equal to the weight of the fluid, wholly or partially, displaced by the object. The corresponding equation is given by, Fb = ρ X g X V Where, Fb is the buoyant force (or thrust) ρ is the density of the fluid in which the object is immersed V is the volume of the object that is submerged in the fluid g is the acceleration due to gravity Apparent loss of weight = Weight of the displaced liquid This apparent loss of weight is the thrust or buoyant force (Fb).
Hot Air Balloon The atmosphere is filled with air that exerts buoyant force on any object. A hot air balloon rises and floats due to the buoyant force. It descends when the balloon’s weight is higher than the buoyant force. It becomes stationary when the weight equals the buoyant force. Ship A ship floats on the surface of the sea because the volume of water displaced by the ship is enough to have a weight equal to the weight of the ship. A ship is constructed in a way so that the shape is hollow to make the overall density of the ship lesser than the seawater. Therefore, the buoyant force acting on the ship is large enough to support its weight.
An incompressible fluid is one which has a constant density throughout the fluid.
The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant. Bernoulli’s Principle?
BERNOULLIS EQUATION DERIVATION
VENTURIMETER
Water enters a horizontal pipe of non-uniform cross-section with a velocity of 0.6m/s and leaves the other end with a velocity of 0.4m/s. At the first end, pressure of water is 1600N/m2 . Calculate the pressure of water at the other end. Density of water = 1000 kg/m3 ?
where, ρ is the density of water = 1000kg/m3 v1 is the velocity at first point = 0.6m/s P1 is the pressure at first point = 1600N/m2 v2 is the velocity at second point = 0.4m/s P2 is the pressure at second point = ?
An airplane wing is designed so that the speed of the air across the top of the wing is 251m/s when the speed of the air below the wing is 225m/s. The density of air is 1.29kg/m3 . What is the lifting force on a wing of area 24m2 ?.
Speed of the air below the wing v1 = 225m/s Speed of the air above the wing v2 = 251m/s Density of the air ρ = 1.29kg/m3 Let P1 and P2 be the pressures below and above the wing respectively. Then the change in pressure provides the net upward force.