## Archive for the ‘FLUID MECHANICS’ category

### some important basics required to study Fluid Mechanics

November 10, 2012

### Fluid Kinametics

September 18, 2011 Fluid Kinematics : – Lines of flow , velocity field and acceleration, Continuity Equation. (1D, 3D), Stream function and velocity potential function Fluid Dynamics : – Bernoulli’s equation, Venturimeter, Orifice meter, Pitot tube What do you mean by dimension of flow? A fluid flow is said to be one, two or three dimensional depending upon the number of independent space coordinates. When is a flow considered steady? A flow is considered steady when the dependent fluid variables at any point do not change with time. When is the flow regarded as unsteady? Give an example for unsteady flow (AU MO3). When the fluid is regarded as unsteady if the dependent variable change with time at a position in the flow. The example for unsteady flow is flow at varying rates through a duct. Differentiate uniform and non uniform flow. When velocity of fluid at any instant of time do not change from point to point in a flow field, the flow is said to be uniform. What is the difference between laminar and turbulent flow. In the laminar flow the fluid particles move along smooth paths in laminar (or) layers with one layer gliding smoothly over the adjacent layer. In turbulent flow the fluid particles move in a very irregular path causing an exchange of momentum from one portion of the fluid to the another. The turbulence setup greater shear stress throughout the fluid and causes more irreversibility and losses. Differentiate compressible and incompressible flow. Compressible flow is that type of flow in which the density of the fluid change from point to point. Incompressible flow is that type of flow in which the density is constant for the fluid flow. r = constant. Distinguish rotational and irrotational flow. Rotational flow is that type of flow in which the fluid particles while flowing along stream lines also rotate about their axis. If the fluid particles while flowing along stream lines, do not rotate about their own axis that type of flow is called irrotational flow. What are streamlines? A stream line at any instant can be defined as an stationary curve in the flow field so that at any point represents the direction of the instantaneous velocity at that point. The streamlines are defined by What are path lines? A path line is the actual path traversed by given fluid particle with the passage of timefrom initial time to final time. The path lines are defined by What are streak lines? A streak line at any instant of time is the locus of the temporary location of all particles that have passed through a fixed point in the flow field. Define convective and local acceleration. Convective acceleration is the instantaneous space rate of change of velocity, Local acceleration is the local time rate change of velocity. Write the one dimensional continuity equation for compressible fluid flow. Continuity equation for compressible fluid flow is mo = r1A1 u1 = r2A2 u2 r1, r2 – density at section 1 & 2 A1, A2 – area at the section 1 & 2, u1, u2 – velocity at section 1 & 2. Define stream function. It is defined as the scalar function of space and time, such that its partial derivative with respect to any direction gives the velocity component at right angles to that direction. State the properties of stream function. i) If stream function exists , it is a possible case of fluid flow. ii) If stream function satisfies the laplace equation is a possible case of irrotational flow. Define velocity potential function. It is defined as a scalar function of time and space such that its negative derivative with respect to any direction gives the fluid velocity in that direction. State the properties of velocity potential function. *If the velocity potential function exists , it is a possible case of irrotational flow. *Lines of constant velocity potential function and lines of constant stream function are mutually orthogonal. What is a flow net? A mesh or net work of stream lines and equipotential lines is called a flow net. Write the applications and limitation of flow net? *It is used to determine the direction of flow and velocity at any point in the closed system *To determine the pressure distribution for given boundaries of flow. Define circulation. Circulation is defined as the flow along a closed curve. Mathematically circulation is obtained if the product of the velocity component at any point and the length of small element containing that point is integrated around the curve. State Bernoulli’s theorem. Bernoulli’s theorem states that in a steady flow of ideal incompressible fluid, the sum of pressure head, velocity head and potential head is constant along a stream line provided no energy is added or taken out by external source. What are all the assumptions taken when deriving the Bernoulli’s equation. Write the Bernoulli’s equation and explain the terms. i. Fluid is ideal and incompressible. ii. flow is steady iii. Flow is along the stream line ie. One dimensional. iv. The velocity is uniform over the section and is equal to mean velocity. v. The only forces acting on the fluid are the gravity forces and pressure forces. Write the Bernoulli’s equation and explain the terms. Bernoulli’s equation is (p/density*g)+(U2/2g)+Z=constant The first term is the flow energy per unit weight (or) pressure head .The second term is the kinetic energy per unit weight (or) kinetic head. The third term Z is the potential energy per unit weight (or) potential head. The sum of these terms is known as total head. Water if flowing through a pipe of 10 cm diameter under a pressure of 19.62 N/cm2 with mean velocity of 3m/s. Find the total head of water at a cross section, which is 8m above the datum line. The pressure (p) = 19.62 N/cm2 = 19.62 x 104 N/m2 ; velocity U = 3m/s Datum head Z = 8 m density of water r = 1000 kg /m3 Total head = (p/rg) + (U2/2g) + Z = [(19.62×104)/(100×9.81)] + [32/(2×9.81)] + 8 = 28.46 m of water. Write few applications of Bernoulli’s equation. *flow through venturimeter * flow through orifice meter *flow through orfices & mouth pieces *flow over notches & weirs What is venturimeter and name the parts of venturimeter? A venturimeter is a device used for measuring the rate of a flow of fluid through a pipe. It consists of three parts i) short converging part ii) throat iii) Diverging part. It is based on the principle of Bernoulli’s theorem. What is a pitot tube and write its principle. Pitot tube is a glass tube bent at right angle . When it is placed in a flow, the liquid raises up in the tube due to conversion of kinetic energy into pressure energy. This raise is used to measure the velocity of flow at a point in the pipe or channel.Dimensional analysis, Models & Similitude  Give the dimensions of the following quantities, a) Pressure b) Surface tension c) dynamic viscosity d) kinematic viscosity. a) Pressure – M L-1 T-2 b) surface tension – M T-2 c) dynamic viscosity– M L-1 T-1 d) Kinematic viscosity– L2 T-1  State the Buckingham’s-p theorem. Buckingham’s-p theorem states n quantities with in base dimensions can generally be arranged to provide only (n-m) independent dimensionless parameters also referred as p terms.  what do you mean by repeating variables? How are the repeating variables selected for dimensional analysis ? In dimensional analysis, it is necessary to recognize the common variables for grouping. These common variables are known as repeating variables. The repeating variables should be chosen in such a way that one variable contain geometric property, other variable contains flow property and third contains fluid property. Normally the characteristic length (L), the velocity (u) and the density are chosen.  Show that the ratio of inertia force to viscous force gives Reynolds number, Inertia force = mass x acceleration = r L3 u /t = r L2 (ut) u /t = r L2 u2 Viscous force = shear stress x surface area = m (u/L) L2 = m uL ratio = (r L2 u2) / (m uL) = r u L / m = Reynolds Number.  What is a Mach number? Mention its field of use. The Mach number is the square root of ratio of inertia force to the elastic force  For surface tension and capillarity studies which dimensionless number is used? The surface tension forces are associated with Weber number Weber Number = inertia force/surface tention force So for surface tension and capillarity studies Weber number is used.  Mention any two applications of Euler’s number. i) flow through hydraulic turbines and pumps ii) flow over submerged bodies iii) flow through penstocks. Name the three types of similarity. a) geometric similarity b) Kinematic similarity c) Dynamic similarity. What is geometric similarity? Geometric similarity concerns the length dimensions. A model and prototype are geometrically similar if and only if all body dimensions in all three coordinates have the same linear scale ratio. scale ratio = Lm/Lp In fluid flow , what does dynamic similarity mean ? Dynamic similarity exists when the model and prototype have the same length scale ratio, time scale ratio and force scale ratio. So the forces at homogeneous points are related through a constant called the force ratio. Estimate the speed of rotation of a 3m diameter propeller to cruise at 10m/s if a 1/16 scale model provided the following results. U = 5m/s N = 750rpm The dynamic similitude requires (Nd)/U to e equated for model and the prototype The speed of rotation = Np = (150 x 10 )/(5 x 10) = 150 rpm.

### Fluid Machines – Pumps and Turbines

September 18, 2011 What is a fluid Machine ? A fluid machine is a device which converts the energy stored by a fluid in to mechanical energy or work.   What are positive displacement machines ? The machine functioning depend essentially on the change of volume of a certain amount of fluid within the machine. There is a physical displacement of the boundary of certain fluid hence it is called positive displacement machine.  Based on the direction of fluid flow how are the fluid machines classified ? According to the flow direction of fluid, the fluid machines are classified as Axial flow machines – The main flow direction is parallel to the axis of the machine. Radial flow machines – The main flow direction is perpendicular to the axis of the machine ie. in radial direction Mixed flow machines – The fluid enters radially and leaves axially or vice-versa.  What is a turbine ? A turbine converts the energy of the fluid in to mechanical energy which is then utilized in running a generator of a power plant.  State the difference between impulse and reaction turbines ? At the inlet of the turbine the energy available is only kinetic energy, the turbine is known as impulse turbine. If the inlet of the turbine, possesses kinetic energy and pressure energy, the turbine known as reaction turbine.  What are Homologous units ? In utilizing scale models in designing turbo machines, geometric simililitude is necessary as well as geometrically similar velocity diagrams at entrance and exit from impellers. Two geometrically similar units having similar vector diagrams are called homologous units.  Define specific speed based on power. The specific speed (Ns ) of turbine is defined as the speed of some unit of series of such size that it produces unit power with unit head. .  Define specific speed based on discharge. The specific speed ( Ns ) of the pump is defined as the speed of some unit of the series of such size that it delivers unit discharge at unit speed  What is the significance of specific speed ? The specific speed inversely proportional to the head across the machine. So low specific speed corresponds to high head across it and vice-versa. The specific speed is directly proportional to the discharge through the machine or power produced by the machine. So low specific speed therefore refers to low discharge or low power machine and vice-versa.  Name the main parts of a radial flow reaction turbine ? i) Casing ii) Guide vane iii) Runner iv) Draft tube.  What is the purpose of the guide vanes in radial flow reaction turbine ? The purpose of the guide vane is to convert a part of pressure energy of the fluid at its entrance to the kinetic energy and then direct the fluid on to the number of blades.  What is a draft tube ? In which turbine it is mostly used. The draft tube is a conduit which connects the runner exit to the trail race, when water is being finally discharged from the turbine. In reaction turbine , the draft tube is mostly used.  What is the primary function of a draft tube ? The primary function of the draft tube is to reduce the velocity of the discharged water to minimize the loss of kinetic energy at the outlet.  Name the main parts of Kaplan turbine. i). Scroll casing ii). Guide vanes iii). Hub with vanes iv). draft tube  Name the main parts of pelton wheel . i) Nozzle ii) Runner with buckets iii) Casing.  An inward flow reaction turbine running at 250rpm has D1 = 1m, b1 = 0.2m, D2 = 0.5m and b3 = 0.3m. If the water enters the wheel radially at 3.5m/s velocity, determine the discharge and velocity of the flow at the outlet. Assume vane thickness at the extremities to be negligible. Q = p D1 b1 Uf1 = p D2 b2 Uf2 = p x 1 x 0.2 x 3.5 = 2.199 m3/s Uf2 = 2.99/ (p x 0.5 x 0.3) = 4.666 m/s  What are the different performance characteristic curves ? i) Variable speed curves (or) main characteristics ii) Constant seed curves (or) operating characteristics iii) Constant efficiency curves (or) Muschel characteristics  Give an example for a low head turbine , a medium head turbine and a high head turbine. Low head turbine – Kaplan turbine Medium head turbine – Francis turbine High head turbine – Pelton wheel.  what are the purposes of casing of a centrifugal pump i) To provide water to and from the impeller ii) To partially convert the kinetic energy in to pressure energy  What are the different types of casing in centrifugal pump ? i) Volute casing ii) Turbine casing (or) casing with guide blades  What is a positive displacement pump ? In the case of positive displacement pumps, the fluid is physically pushed from an enclosed space. The positive displacement pumps can be either reciprocating type or rotary type.  Where is the reciprocating pump well suited ?> The reciprocating pump is well suited for relatively small capacities and high heads.  what are the main components of a reciprocating pump ? 1)cylinder 2) Piston 3) suction valve 4) Delivery valve 5) Suction pipe 6) delivery pipe 7) crank shaft and connecting rod mechanism.  Define coefficient of discharge of reciprocating pump. The ratio between the actual discharge and theoretical discharge is known as coefficient of discharge. Cd = Qact / Qthe.  Define slip of the reciprocating pump. When does the negative slip occurs ? The difference between theoretical discharge and actual discharge is called the slip of the pump. Slip = Qthe. – Qact , % of slip = (Qthe. – Qact ) x 100 / Qthe. Negative slip occurs when delivery pipe is short suction pipe is long and pump is running at high speed.  Differentiate between single acting and double acting reciprocating reciprocating pump. In single acting pump, there is one suction valve and one delivery valve. On the backward stroke of the piston, the suction valve opens and water enters into the cylinder space. On the forward stroke, the suction valve closes and delivery valve opens, the water is forced through the delivery pipe. In the double acting pump, there are two suction valves and two delivery vales one in the front and one in the rear. When the piston moves backward, the suction valve in the front opens and delivery valve in the rear opens and water is forced through it. When the piston moves forward, the suction valve in the rear opens and delivery valve in the front opens and water is forced through it.  What is an indicator diagram of a reciprocating pump ? The indicator diagram of a reciprocating pump is the diagram which shows the pressure head in the cylinder corresponding to any position during the suction and delivery strokes.  A single acting single cylinder reciprocating pump has the following characteristics. Discharge = 6 lps, suction head = 4m, Delivery head = 20m, Find the energy required to drive the pump. Energy required = r g Q ( Hs + Hd ) Watts = (1000 x9.81 x 6×10-3 x (4 + 20) / 1000 = 1.409 kW.  What is an air vessel and what is its purpose ? An air vessel is a closed chamber connected on the suction or delivery or both sides of the reciprocating pump to obtain a more uniform flow.  Name some rotary positive displacement pumps. a. Gear pumps. b. Vane Pumps. c. Piston pumps. d. Screw pumps.

### Introduction | Fluid Mechanics | Fluid properties

September 16, 2011

### Fluid Mechanics – Introduction Fluid Mechanics is that section of applied mechanics, concerned with the statics and dynamics of liquids and gases.

A knowledge of fluid mechanics is essential for the Mechanical engineer, because the majority of Mechanical processing operations are conducted either partially or totally in the fluid phase.

The handling of liquids is much simpler, much cheaper, and much less troublesome than handling solids.

Even in many operations a solid is handled in a finely divided state so that it stays in suspension in a fluid.

Fluid Statics: Which treats fluids in the equilibrium state of no shear stress

Fluid Mechanics: Which treats when portions of fluid are in motion relative to other parts. Fluids and their Properties

Fluids

In everyday life, we recognize three states of matter:

• solid,
• liquid and
• gas.

Although different in many respects, liquids and gases have a common characteristic in which they differ from solids: they are fluids, lacking the ability of solids to offer a permanent resistance to a deforming force.

fluid is a substance which deforms continuously under the action of shearing forces, however small they may be.Conversely, it follows that:
If a fluid is at rest, there can be no shearing forces acting and, therefore, all forces in the fluid must be perpendicular to the planes upon which they act.

Shear stress in a moving fluid

Although there can be no shear stress in a fluid at rest, shear stresses are developed when the fluid is in motion, if the particles of the fluid move relative to each other so that they have different velocities, causing the original shape of the fluid to become distorted. If, on the other hand, the velocity of the fluid is same at every point, no shear stresses will be produced, since the fluid particles are at rest relative to each other.