CE MECHANICS OF FLUIDS UNIT I


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1 CE MECHANICS OF FLUIDS UNIT I 1. Define specific volume of a fluid and write its unit [N/D14][M/J11] Volume per unit mass of a fluid is called specific volume. Unit: m3 / kg. 2. Name the devices that are used to measure the pressure of a fluid. [N/D14] The Device used to measuring Fluid Pressure, by the Gauges is, Piezometer Tube.Manometer.
2 3. Calculate the specific weight, density and specific gravity of 1 litre of liquid which weighs 7 N. [M/J11] [A/M15] Solution: State the concept of pressure measurement used in mechanical gauges [M/J09] [A/M15] Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure and display pressure in an integral unit are called pressure gauges or vacuum gauges. A manometer is a good example as it uses a column of liquid to both measure and indicate pressure. Likewise the widely used Bourdon gauge is a mechanical device which both measures and indicates, and is probably the best known type of gauge. A vacuum gauge is an absolute pressure gauge used to measure the pressures lower than the ambient atmospheric pressure. Other methods of pressure measurement involve sensors which can transmit the pressure reading to a remote indicator or control system.
3 5. Define Centre of Pressure [N/D14] [M/J16] The center of pressure is the point where the total sum of a pressure field acts on a body, causing a force to act through that point. The total force vector acting at the center of pressure is the value of the integrated vectorial pressure field. The resultant force and center of pressure location produce equivalent force and moment on the body as the original pressure field. Pressure fields occur in both static and dynamic fluid mechanics. 6. Temperature rise, decrease viscosity in liquids but increases it in gases, why? [M/J11] Viscosity is nothing but nature of fluid due to which it offers resistance to gradual deformation. In case of liquid,liquid molecules are bonded by inter molecular force of attraction and when we increase the temperature, this force of attraction gets weaken causing dissociation of bond and molecules becomes more freely to flow/move, causing decrease in viscosity of liquid ( viscosity of liquid is due cohesion of liquid molecules i.e. tendency of similar particle to cling one another ),whereas in case of gases,gaseous molecules do have weak vander wall force of attraction, as we increase the temperature, energy (in the form of heat ) transfers to gas molecules, which increase the randomness of molecules and molecules starts colliding with each other,retarding the motion of gases,resulting increase in viscosity of gases. 7. State Newton s Law of Viscosity. [M/J10] It states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality is called the coefficient of viscosity. 8. Name the Types of fluids. [M/J09] 1. Ideal fluid 2. Real fluid 3. Newtonian fluid 4. NonNewtonian fluid. 5. Ideal plastic fluid
4 9. Define Surface Tension. [A/M11] Surface tension is defined as the tensile force acting on the surface of a liquid in contact with a gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension. Unit: N / m. 10. Define Capillarity [N/D10] Capillary is defined as a phenomenon of rise of a liquid surface is a small tube relative to adjacent general level of liquid when the tube is held vertically in the liquid. The resistance of liquid surface is known as capillary rise while the fall of the liquid surface is known as capillary depression. It is expressed in terms of cm or mm of liquid.
5 1. A Liquid has a specific gravity of Find its density, specific weight and also the weight per liter of the liquid. If the above liquid is used for lubrication between a shaft and a sleeve, find the power lost in liquid for a sleeve length of 100 mm. The diameter of the shaft is 0.5 m and the thickness of the liquid film is 1 mm. Take the viscosity of fluid as 0.5 Ns/m 2 and the speed of the shaft as 200rpm. [N/D11] [N/D14] Sol: Volume V = 1 litre = m 3 Specific gravity S = 0.72 (i) Density ρ = S * 1000 = 0.72 * 1000 = 720 kg/m 3 (ii) Specific weight W = ρ*g = 720 * 9.81 = N/m 3 (iii) Weight w = W*V = * = N (iv) µ = 0.5 Ns/m 2 Diameter D = 0.5 m Speed of shaft N = 200 rpm Sleeve length L = 100 mm Thickness of oil film t = 1 mm u = (πdn) / 60 = (π*0.5*100)/60 = 2.62 m/s du = 2.62 m/s dy = 1mm = m τ = µ (du/dy) = 0.5 * (2.62/0.001) = 1310 N/mm 2 F = τ * A = 1310 * πdl = N Torque T = F * D/2 = * 0.5/2 =51.44 Nm Power lost = 2πNT/60 = (2*π*100*51.44)/60 = W
6 2. If the velocity distribution over a plate is given by u = 2/3 y y 2 in which u is the velocity in metre per second at a distance y metre above the plate, determine the shear stress at y = 0 and y = 0.15m. Take dynamic viscosity of fluid as 8.63 poise. [M/J09][N/D14]
7
8 3. A 150mm diameter vertical cylinder rotates contacted to the another cylinder of diameter 151 mm. Both the cylinder are 250mm high. If the torque of 12 Nm is required to rotate the inner cylinder at 100 r.p.m. determine the viscosity of the fluid in the space between the above two cylinders. [N/D14] [A/M15]
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10 4. Determine the total pressure on a circular plate of diameter 1.5 m which is placed vertically in water in such a way that the center of the plate is 3 m below the free surface of water. Also find the position of centre of pressure. [N/D09] [M/J08] [A/M15]
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12 5. (i) Differentiate (1) Real fluids and ideal fluids (2) Newtonian and nonnewtonian fluids (ii) What is the difference between U tube differential manometer and inverted U tube differential manometer? [M/J12] [N/D16] (1) Real Fluid: A fluid, which possesses viscosity, is known as real fluid. All fluids, in actual practice, are real fluids. Ideal Fluid: A fluid, which is incompressible and is having no viscosity, is known as an ideal fluid. Ideal fluid is only an imaginary fluid as all the fluids, which exist, have some viscosity. (2) Newtonian fluids 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. NonNewtonian fluids You can probably guess that nonnewtonian fluids are the opposite of Newtonian fluids. When shear is applied to nonnewtonian fluids, the viscosity of the fluid changes. (3) UTube Manometer: It consist a U shaped bend whose one end is attached to the gauge point A and other end is open to the atmosphere. It can measure both positive and negative (suction) pressures. It contains liquid of specific gravity greater than that of a liquid of which the pressure is to be measured. Inverted UTube Manometer: Inverted UTube manometer consists of an inverted U Tube containing a light liquid. This is used to measure the differences of low pressures between two points where where better accuracy is required. It generally consists of an air cock at top of manometric fluid type.
13 6. If the velocity profile of a liquid over a plate is a parabolic with the vertex 20 cm from the plate, where the velocity is 120 cm/sec. calculate the velocity gradients and shear stress at a distance of 0, 10 and 20 cm from the plate, if the viscosity of the fluid is 8.5 poise. [A/M11] [N/D09] [M/J13]
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