University:
Liverpool John Moores University
Course:
7003LBSIBM | International Business Management
Academic year:

2024
Views:

298

Pages:

20
Author:

jay k

10 Mechanical Properties of Fluids → Fluids: The materials which can flow from one place to another place are called fluids → Liquids: A liquid has definite size but not definite shape → Gas: A gas is highly Compressible A gas has neither definite shape nor a definite Size → Fluid Thrust: The normal force exerted by the fluids at rest on a surface in contact with it → Fluid Pressure: Fluid thrust per unit aka Fluid pressure = Fluid Thrust / Area [F/A] → Dimensional formula [ML^-1T^-2] → Pressure is a scalar quantity → CGS units is dyne/cm² → Practical application of pressure → knife → A sharp knife cut better than a blunt one → camel can walk fastly in a sand in desert although the force applied in both the cases is same → Density: It is defined as mass per unit volume of the substance Density = mass / volume SI unit = kg/m³ Dimensional formula [ML^-3T^0] Relative density. It is defined as the ratio of density of substance to the density of water at 4°C. Relative density = Density of substance / Density of water at 4°C • Relative density is known as Specific gravity It has no unit and it is a dimensionless physical quantity Note: The density of water at 4°C is 1 g/cm³ = 1000 kg/m³ STP means Standard Temperature (0°C or 273K) & 1 atmospheric pressure → find the relative density of aluminium having density 2.7 x 10^3 kg/m³ Relative density = density of aluminium / density of water at 4°C = 2.7x10^3 / 1000 = 2.7x1000 / 1000 = 2.7 31 →Expression for pressure at a point inside a liquid Consider a fluid at rest having density (ρ). in fluid of cross sectional area (A) & height (h) Let P1 and P2 be fluid pressure at top and bottom respectively. Pressure at As fluid cylinder is at rest the resultant horizontal & vertical force should be ... So, Various force acting on vertical direction A force due to the fluid pressure at the top (P1A) weight of a fluid cylinder acting downwards (mg) m=ρV=ρAh Force due to fluid pressure at bottom F2=P2A fluid cylinder is in eqm net downward force = net upward force F1+mg=F2 P1A+ρAhg=P2A P2-P1=ρhg P2=P1+ρhg Note: P1=Pa (Pa atmospheric pressure) & P2=P P=Pa+ρhg On what factors pressure difference of a cylindrical fluid element inside a fluid depends The pressure difference depends on a) The vertical height b) Acceleration due to gravity c) Density of fluid Gauge Pressure: The excess of pressure at a depth (h) in a liquid is called Gauge pressure at that point P-Pa=ρgh Image Analysis Textual Content: 5 Mercury barometer A mercury barometer is a device to measure atmospheric pressure It is designed by Torricelli. E A long glass tube closed at one end & filled caith mercury is inviertes into a turn Dough (vester) of maculy so we find that a mercury Colum in the lube has height of above 76cm above the mercury level at shown in fig. If the tube is rised, toweled ved inclined in mercury through the vertical height of mercury is Constant Plon fis \[P_{Eh}-F_{R}=P_{0}h\] \[(\mathcal{P}_{B=0})\] Atmospheric Pressure Palgh deneity of mercity \(f=13~6\times10^{3}Kg/e^{2}\) \[q=9kn1z^{2}\] \[h=.7ha a Archimedes Principle. When a body is immersed partially (or) completely in a liquid at rest it experiences an upthrust. The upthrust is equal to a weight of the liquid displaced by the body → Fluid statics: The branch of physics that deals with the study of fluids at rest. → Fluid dynamics: The branch of physics that deals with the study of fluids in motion. → Stream line flow (SL): Study flow when all liquid flows such that each particle of the liquid moves along the same path & same velocity Ex: Flow of water through a Capillary tube. In stream line flow, no two stream lines can cross each other. → Turbulent flow: The flow of fluids in which velocity of all particles crossing a given point is not same & motion is irregular. → Critical Speed: The maximum speed of a flow of liquid above which a stream line becomes turbulent flow Difference between Stream Line flow & turbulent flow Stream Line flow Turbulent flow It is a regular flow Turbulent flow is an of liquid irregular flow of liquid The velocity of all particles the velocity of all particles is same at a given point is different at a given point • Every Liquid particles. moves with velocity less. han Critical Speed. Every Liquid particles. moves with velocity. greater than Critical Speed. Equation of Continuity- Statement: The mass (m) entered at one end. of the tube of uniform cross section is equal to mass leaving from other & end of the tube A Consider han viscous Liquid flowing h/w 2 Section AE, DOF tube. AB Let A1 be the area of cross-section be the fluid velocity al'a & A-A be the area of cross section & ly be the Fluid velocity ag e →Density, P= m= PV volume; V=AL VEAL VEAVAL M-PAVAT how mass of fluid at Point A, [m_{1}=P_{A}V_{1}\Delta t-0] how mass of fluid at Point B, [m_{2}=P_{A}V_{2}\Delta t-2] from conservation of mass from eq ① & ② ⇒ m₁ = m₂ [P_{A}V_{1}\Delta t=P_{A}V_{2}\Delta t] [⇒A_{1}v_{1}=A_{2}v_{2}|] → Ideal Fluid: An ideal fluid is one in which it non viscous incompressible, irrotational & steady flow. → Bernoulli's Principle: For a streamline flow of ideal fluid, Sum of Pressure energy, KE & PE per Unit Volume of flow remains constant P+ 1/2 pv² + pgh = constant Proof: Let P₁, A₁, V₁, h₁, & P₂, A₂, V₂, h₂ be the Pressure, area of cross section, velocity of &, height at Points A & B as shown in fig. work done at 'A' w₁ = P₁A₁v₁dt work done at 'B' w₂ = P₂A₂v₂dt Net work done on fluid Pressure energy →Δw = w₁ - w₂ Δw = P₁A₁v₁dt - P₂A₂v₂dt