"BASIC FLUID MECHANIS" Course Overview _ S. M. Talha Jubaed

AMIE Engineering Study Room

February 11

আজ থেকে "BASIC FLUID MECHANIS" Course নিয়ে ্পযায়ক্রমে আলোচনা করবো। প্রতিটি অধ্যায় নিয়ে একদিন একদিন করে আলোচনা করবো, আজ ১ম অধ্যায়ে যা যা পড়তে হবে টা দেওয়া হল । আশা করি আপনাদের কাজে লাগবে।

Properties of Fluidsঃ

১. State and Explain Newton’s Law of viscosity. How can the dimensions of viscosity be derived from it? Oct-09; Oct-07; Mar07; Sep04; Sep03; Oct02; May00 

২. Differentiate between Newtonian fluid and non-Newtonian fluid. Apr08

৩. Define kinetic viscosity, dynamic viscosity, surface tension, capillarity and manometry, Viscosity Index. Mar06; Sep04; Sep03;

৪. Define Newtonian, Non-Newtonian and plastic fluids. Show them on a shear-stress vs. velocity gradient plot. Sep05 Apr02

৫. Explain pressure, specific weight, Bulk modulus of elasticity with reference to fluid. Oct-08; Mar-06; Oct02; Apr02;

Mathematical:

১. A plate having an area of 0.6 m2 is sliding down the inclined plane at 30° to the horizontal with a velocity of 0.36 m/s. there is a fluid film of 1.8 mm thick between the plane and the plate. Find the viscosity of the fluid if the plate weights 280 N. 10 Marks. Mar07[Similar to No-11 Question]

২. The velocity distribution for flow over a plate given by u=2y-y^2 where u is the velocity in m/s at a distance y meters above the plate. Determine the velocity gradient and the shear stress at the boundary and 0.15 m from it. 6 Marks Sep-03[Similar to No-3 Question]

৩. The velocity distribution over a plate is given by u=3/2 y-1/2 y^2. If the viscosity of the fluid is 8 poise, find the shear stress at the plate boundary and at y = 0.15 m from the plate. 10 Marks Apr-03 [Similar to No-2 Question]

৪. The velocity distribution of flow over a plate is parabolic with vertex 30 cm from the plate, where the velocity is 180 cm/s. if the viscosity of the fluid is 0.9 N-s/m2 find the velocity gradient and shear stresses at distances of 0, 15 and 30 cm from the plate. 15 Marks Sep-05

৫. A 25 cm diameter horizontal disk rotates at a distance of 2 mm above a solid surface. Water at 10℃ (μ=1.308 × 〖10〗^(-3 ) N-s/m^2 and ρ=999.7 kg/m^(3 )) fills the gap. Estimate the torque required to rotate the disk at 400 rpm. Any equation used in the calculation should be derived from the law of viscosity. 12 Marks Oct-09[Similar to No-6 Question]

৬. A 120mm disc rotates on a table separated by an oil film of 1.8 mm thickness. Find the viscosity of oil if the torque required to rotate the disc at 60 rpm is 3.6 × 〖10〗^(-4) Nm. 15 Marks Sep-06 [Similar to No-5 Question]

৭. Two large fixed parallel planes are 240 mm apart. The space between the surfaces is filled with oil of viscosity 0.81 N-s/m2. A flat thin plate of 0.5 m2 area moves through the oil at a viscosity of 0.6 m/s. calculate the drag force (i) when the thin plate is equidistant from the fixed planes and (ii) when the plate is at a distance of 80 mm from one of fixed planes. 14 Marks Sep-04; Dec-00; [Similar to No-6 (extra) Question]

৮. A piston 59mm diameter rotates concentrically inside a cylinder of 60 mm diameter. Both the piston and the cylinder are 80mm long. Find the rpm of the piston if the space between the cylinder and the piston is filled with oil of viscosity 0.3 N.s/m2 and a torque of 1.5 Nm is applied. Find the power required to rotate the piston. 10 Marks. Mar-04[Similar to No-10 Question]

৯. A square metal plate 1.5 m side and 1.5 mm thick weighting 50 N is to be lifted through a vertical gap of 25 mm of infinite extent. The oil in the gap has a specific gravity of 0.95 and viscosity 2.5 N-s/m2. If the plate is to be lifted at a constant speed of 0.1 m/s, find the force and power required. 10 Marks Nov-01

১০. A cylinder of 0.12 m radius rotates concentrically inside a fixed cylinder of 0.13m radius. Both cylinders are 0.3m long. Determine the viscosity of the liquid which fills the space between the cylinders if a torque of 0.880 Nm is required to maintain an angular velocity of 2π rad/s. 10 Marks Dec-00 [Similar to No-8 Question]

১১. A cubical block weighting 20 kg and having a 20 cm edge is allowed to slide down on an inclined plane surface making an angle of 20° with the horizontal on which there is a thin film having a viscosity of 0.22× 10-3 kg.sec/m2. What terminal velocity will be attained if the film thickness is estimated to be 0.025 mm? 10 Marks May-00[Similar to No-1 Question]

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Extra for A+ Desired Student:

১. What is Fluid Mechanics? Define Fluid, Compressibility, Cohesion, and Adhesion.

২. What is Ideal Fluid? What are the characteristics of an ideal fluid?

৩. A 150 mm diameter shaft rotates at 1500 rpm in a 200 mm long journal bearing with 150.5 mm internal diameter. The uniform annular space between the shaft and the bearing is filled with oil of dynamic viscosity 0.8 poise. Calculate the power dissipated as heat. AMIE(I)-01

৪. A circular disc of diameter D is slowly rotated in a liquid of large viscosity at a small distance from a fixed surface. Derive an expression of torque necessary to maintain an angular velocity. AMIE (I)-02

৫. A fluid has an absolute viscosity of 0.048 Pas and a specific gravity of 0.913. for flow of such a fluid over a solid flat surface, the velocity at a point 75 mm away from the surface is 1.125 m/s. calculate the shear stresses at the solid boundary and also at points 25 mm, 50 mm and 75 mm away from the surface in normal direction, if the velocity distribution across the surface is (i) linear (ii) parabolic with vertex at the point 75 mm away from the surface. AMIE (I)-00

৬. A central plate of area 6 m2 being pulled with a force of 160 N. if the viscosities of the two oils are in the ratio of 1:3 and the viscosity of top oil is 0.12 N.s/m2. Determine the velocity at which the central plate will move, [Similar to No-7 Question]

৭. If the pressure difference between the inside and outside of the air bubble of diameter 0.01 mm is 29.2 kPa, what will be the surface tension at air-water interface? AMIE (I)-00

৮. Gas A is compressed isothermally and gas B at 100 kPa is compressed isentropic ally (γ=1.4). Which gas is more compressible? AMIE(I)-99

সাধারন আলোচনাঃ শুধুমাত্র পাশ করার জন্য (40-50% মার্কস পাবার জন্য ) *** পর্যন্ত প্রশ্নগুলো পড়তে হবে এবং অংকগুলো করতে হবে। তবে এ+ পাবার জন্য *** এর নিচের অংশও ভালভাবে পড়তে হবে। এই অধ্যায়ের অংকসমূহ খুবই সোজা। দরকার একটু একাগ্রতা আর বারবার অনুশীলন। বেসিক ফ্লুয়িড মেকানিক্স কোর্সটিতে একটু পরিশ্রম করলে খুব সহজেই ভাল মার্কস তোলা সম্ভব। তাই এই কোর্সটি একটু বেশি সময় নিয়ে পড়তে হবে। এই অধ্যায় (Properties of Fluids) থেকে মোটামুটি ২০ মার্কসের উত্তর করা সম্ভব (অর্ধেক পাশ), তাই ১নং শিট এবং এই শিট বেশ ভাল করে পড়তে হবে। বিগত ২০টি পরীক্ষায় এই অধ্যায় থেকে কি পরিমাণ মার্কস এসেছে তা নিচের ছকে দেখানো হলঃ

Exam Marks Exam Marks Exam Marks Exam Marks
May-00 = 20 ;Nov-01 = 10 ;Apr-02 = 25 ;Oct-02 = 08
Apr-03 = 10 ;Sep-03 = 10 ;Mar-04 = 15 ;Sep-04 = 20
Mar-05 = 10 ;Sep-05 = 20 ;Mar-06 = 05 ;Sep-06 = 20
Mar-07 = 10 ;Apr-08 = 08 ;Oct-09 = 12 ;Apr-10 = 20
Dec-00 = 20 ;Oct-10 = 20 ;Apr-11 = 20 ;May-01 = 15

Necessary Laws of this chapter:

১. Shear stress, τ = (Shear force)/Area = F/A

২. Shear stress, τ =μ.du/dy; Where μ = Viscosity; du/dy= Rate of shear stress or rate of shear deformation or Velocity gradient.

৩. Torque, T = Shear stress (τ) × Area (A) × Radius (r).

৪. Angular speed, ω =2πN/60 ; Where N = Number of Rotation per minute (rpm).

৫. Required force, F = W + 2(τ.A); where W = Weight of the plate; τ = shear stress A = Area of the plate.

৬. Required Power, P = Force (F) × Speed (u).

৭. The equation of velocity profile, which is parabolic, is given by ly^(2 )+ my +n; where l, m, n are constants.

৮. Tangential velocity, u =πdN/60; Where d = diameter; N = Number of Rotation per minute (rpm).

৯. Power dissipated as heat = shear force × Tangential velocity

১০. Linear velocity, u= Angular speed × radius =ωr.

১১. Viscous torque = Shearing force × radius.

১২. Drag force, F = F_1+F_2; where F_1 = Shear force on upper side of the plate; F_2= Shear force on lower side of the plate.

১৩. Surface area of the inner cylinder =πdl ; where d = diameter of shaft l= length of each cylinder.

১৪. Pressure force =p×π/4 d^2; Where p= pressure; d = diameter

১৫. Surface tension force acting around the circumference= σ×πd; where σ= Surface tension.

১৬. p×π/4 d^2= σ×πd

Note: এই অধ্যায়ের অংকসমূহ করার জন্য এই সূত্রসমূহ মুখস্থ রাখা খুবই দরকার। এগুলো মুখস্থ থাকলে এই অধ্যায়ের যেকোন অংক করাটা সহজ হয়ে যাবে।