### Fluid mechanics assignment

• 1. ASSIGNMENT 1 Ques.(1) State and prove the Pascal,s law? Ans. Pascal's law states that the pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and the walls of the container, as P=F/A. Where P is the pressure, F is the normal component of the force and A is the Area. Let us imagine an arbitray right angled prismatic volume in the liquid of density ρ in equilibrium. The ares of these faces ABFE, ABDC and CDFE are ad, bd and cd respectively. Let the pressure of liquid on faces ABFE, ABDC and CDFE P1 , P2 , and P3 respectively. The pressure of liquid exerts the force normal to the surface. Let us assume pressure P1 exerts the Forece F1 on the surface ABFE, pressure P2 exerts pressure of the surface ABDC and pressure P3 exerts force on the surface CDFE. F1 = P1 * Area ABFE = P1 ad F2 = P2 * Area ABDC = P2 bd F3 = P3 * Area CDFE = P3 cd Also, sinθ = b/a and sinθ =c/a Since the prism in the equilibrium, thereofre net force on the prism is zero. Thus F1 sinθ = F2 and F1cosθ = F3 or P1ad(b/a) = P2bd and P1ad(c/a) = P3cd or P1 = P2 and P1 = P3 Hence, P1=P2=P3 Hence the Pascal's law is proved. Ques.(2) What is the difference between dynamic viscosity and kinematic viscosity? State their units of measurements.
• 2. Ans. The main difference between dynamic and kinematic viscosity is that dynamic viscosity is a meausrement of how difficult it is for a fluid to flow whereas kinematic viscosity is the dynamic of a fluid divided by its density. Both dynamic and kinematic viscosity viscosities meausre how diffecult it is for a fluid to flow. Kinematic viscosity measures this in terms of density, whereas dynamic viscosity does not. Units of meausrements:-- Dynamic viscosity has SI Units of PaS. It is more commonly meausred in cintipose (cP). Kinematic viscosity has SI Units as m2 /s. It is more commonly meaused in centistokes (cSt). Ques. (3) Define Newtonian and Non-Newtonian fluids? Ans. A Newtonian fluid's viscosity remains constant, no matter the amount of shear applied for a constant temperature. These fluids have a linear relationship between viscosity and shear stress. Examples:- Water, Mineral oil, Gasoline, Alcohol, etc A Non-Newtonian Fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for example, becomes runnier when shaken and is thus a non-N ewtonian fluid. When shear is applied to non-Newtonian fluids, the viscosity of the fluid changes. The behavior of the fluid can be described one of four ways: (a). Dilatant- Viscosity of the fluid increases when shear is applied. For example: Quicksand, Cornflower and water, sily putty, etc. (b). Pseudoplastic- Pseudoplastic is the opposite of dilatant; the more shear applied, the less viscous it becomes. For example: Ketchup (c). Rheopectic- Rheopectic is very similar to dilatant in that when shear is appled, viscosity increases. The difference here, is that viscosity increase is time-dependent. For example:
• 3. Gypsum paste, cream, etc. (d). Thixotropic- Fluids with thixotropic properties decreases in viscosity when shear is applied. This is a time dependent property as well. For example: Paint, Cosmetics, Asphalt, Glue, etc. Ques. (4) Define the compressibility and bulk modulus? Ans. In thermodynamics and fluid mechanics, compressiblity ( also known as the coefficient of compressibility or isothermal compressibility) is a measure of the relative volume change of a fluid or solid as a response to pressure ( or mean stress) change. In its simple form, the compressibility β may be expressed as β = - 1*∂V/V*∂p where V is the volume and p is the pressure. Bulk Modulous- The Bulk Modulous (K or B) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. K = -V *dp/dV Ques. (5) What is Eulers equation of motion? Ans. The Euler's equation for steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure and density of a moving fluid. It is based on the Newton's Second Law of Motion. The integration of the equation gives Bernoulli's equation in the form of energy per unit weight of the following fluid. It is based on the following assumptions: – The fluid is non-viscous (the frictional losses are zero). – The fluid is homogenous and incompressible ( mass density of the fluid is constant). – The flow is continuous, steady and along the stremaline. – No energy of force (except gravity and pressure forces) is involved in the flow. – The velocity of the flow is uniform over the section. Ques. (6) What is fluid? Ans. A fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases and plasmas. They are substances with zero shear molulous, or, in simpler terms, substances which cannot resist any shear force applied to them. Fluid includes both the liquid and gas phases.
• 4. Ques. (7) Drive Bernoulli equation therom for steady flow of an incompressible fluid? Ans. Firstly we'll look at the assumptions made in the derivation of Bernoulli's equation: – The fluid is ideal, i.e., Viscosity is zero. – The flow is steady. – The flow is incompressible. – The flow is irrotational. It states that in a steady, ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant. The total energy consists of pressure energy, kinetic energy and potential energy or datum energy. These energies per unit weight of the fluid are: Pressure Energy = P/mg Kinetic Energy = v2. /2g Datum Energy = z Mathimatically, the Bernoulli's theorem is as follows: (p/w) + (v2. /2g) + z = constant ASSIGNMENT 2 1-Fluid is a substance that (a) cannot be subjected to shear forces (b) always expands until it fills any container (c) has the same shear stress.at a point regardless of its motion (d) cannot remain at rest under action of any shear force ( e ) flows.
• 5. Correct Answer is:- d ( Cannot remain at rest under action of nay shear force) 2-Fluid is a substance which offers no resistance to change of (a) pressure (b) flow (c) shape (d)volume (e) temperature. Correct Answer is:- c (Shape) 3- Practical fluids (a) are viscous (b) possess surface tension (c) are compressible (d) possess all the above properties (e) possess none of the above properties. Correct Answer is:- d ( Possess all the above properties) 4-In a static fluid (a) resistance to shear stress is small (b) fluid pressure is zero (c) linear deformation is small (d) only normal stresses can exist (e) viscosity is nil. Correct Answer is:- d ( Only normal stresses can exist) 5-A fluid is said to be ideal, if it is (a) in compressible (b) in viscous (c) viscous and incompressible (d) in viscous and compressible (e) in viscous and incompressible. Correct Answer is:- d (in viscous and compressible ) 6- An ideal flow of any fluid must fulfill the following (a) Newton's law of motion (b) Newton's law of viscosity
• 6. (c) Pascal' law (d) Continuity equation (e) Boundary layer theory. Correct Answer is:- d (Continuity equation ) 7- If no resistance is encountered by displacement, such a substance is known as (a) fluid (b) water (c) gas (d) perfect solid (e) ideal fluid. Correct Answer is:- e (Ideal fluid) 8- The volumetric change of the fluid caused by a resistance is known as (a) volumetric strain (b) volumetric index (c) compressibility (d) adhesion (e) cohesion. Correct Answer:- c ( Compressiblity) 9- Liquids (a) cannot be compressed (b) occupy definite volume (c) are not affected by change in pressure and temperature (d) are not viscous (e) none of the above. Correct Answer is:- e (None of the above) 10-Density of water is maximum at (a) 0°C (b) 0°K (c) 4°C (d) 100°C (e) 20°C. Correct Answer is:- c ( 4°C)