Title 4. FLUID MECHANICS WORKSHEETS CW.pdf ✅

IX– Physics (Vol – II) Olympiad Class Work Book FLUID MECHANICS FLUID: A Substance which has no definite shape and has the ability to flow is called Fluid. Example: Liquids and gases 1) The difference between liquids and gases is that liquid cannot be compressed but gas can be compressed and liquids have free surface but gases cannot have any free surface. 2) Fluid mechanics is a branch of physics that deals with the behaviour of fluids at rest and motion. 3) Liquid Statics deals with the behaviour of fluids in rest. 4) Fluid dynamics deals with the behaviour of fluids in motion. DENSITY ( ρ ): Density of a substance is defined as the mass per unit volume. i) Density ( ρ ) mass m = = volume v ii) Its SI unit is kg -3 m iii) Its CGS unit is g -3 cm iv) Its Dimensional formula is 1 -3 0   M L T   v) It is a Scalar vi) -3 -3 1g cm =1000kg m Relative density (R.D): It is defined as the ratio of density of the substance to the density of water at 0 4 C . 0 Density of Substance Relative Density Density of water at 4 C  It is unit less and dimensionless Physical quantity. Density of a mixture of two or more liquids: Case 1: Suppose two liquids of densities 1 ρ and 2 ρ having masses m1 and m2 are mixed together then the density of mixture will be 1 2 1 2 Total mass m + m ρ= = Total Volume V + V

IX– Physics (Vol – II) Olympiad Class Work Book 1 ρα V 1 1 ρ V V 1 = = = ρ V V+dV dP V- V B       -V dP dV = B       1 ρ 1 = ρ dP 1- B where dp= change in pressure B= Bulk modulus of elasticity of the liquid -VdP = dV THRUST: A force acting normally on a surface is called thrust. i) It’s unit in CGS system is dyne. ii) It’s unit in SI System is newton (N). iii) The gravitational unit of thrust is Kilogram force (kgf). iv) Its Dimensional formula is 1 1 -2   M LT  . v) It is a vector quantity. PRESSURE: The force (thrust) acting normally on unit surface area is called pressure. If a thrust F acts on an area A such that P is the pressure. Thrust Pressure = Area F P= A i) Pressure unit in CGS system is 2 Dyne/cm . ii) Its unit in SI system is 2 newton /m .(or) pascal (Pa) iii) Its Dimensional formula 1 -1 -2   M L T   iv) It is a Scalar quantity 2 Nm is also called Pascal (Pa) in the honour of physicist Pascal who discovered law for the transmission of pressure in the fluids.
Olympiad Class Work Book IX – Physics (Vol – II) Pascal: When a force of 1N (thrust) acts normally on an area of 2 1m , then pressure acting on the surface is called 1 Pascal. i) 1 kgf 2 m  =10Pa (approx) ii) 1 bar 5 =10 Pa iii) 1 torr =1mm of Hg Atmospheric Pressure 0 ( P ): It is pressure of the earth’s atmosphere. This changes with weather and elevation. Normal Atmospheric pressure at sea level is 5 1.013×10 Pa . 5 1 atm=1.013×10 Pa Absolute pressure and Gauge pressure: The excess pressure above atmospheric pressure is usually called gauge pressure and the total pressure is called absolute pressure. Thus, Gauge Pressure =absolute pressure-atmospheric pressure ̈Absolute pressure is always greater than or equal to zero. ̈While gauge pressure can be negative also. Pressure in a Fluid: When a fluid (either liquid or gas) is at rest, it exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in t h e fluid. While the fluid as a whole is at rest, the molecules that make up the fluid are in motion, the force exerted by the fluid is due to molecules colliding with their surroundings. If we think of an imaginary surface within the fluid, the fluid on the two sides of the surface exerts equal and opposite forces on the surface, otherwise surface would accelerate and fluid would not be remained at rest. dA dF  dF  Consider a small surface of area dA centered on the fluid, the normal force