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.