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Introduction to Fluid Dynamics IV

Fluid Dynamics Definition


Fluid dynamic is defined as it is that the branch of applied science which deals with the motion or moment and behavior of fluid such as liquid or gas. In physics, it is the sub division of fluid mechanics, which studies the fluid flow.


Fluid Mechanics Examples


Fluid mechanics is the branch of physics that deals with the fluid flow and the force of fluid. Some of the fluid mechanics examples are vortex potential, calculation of flow around the cylinder, find water or petroleum flow through a pipe line , venture flow meter, find the force and movements of aircraft, predicting weather patterns, reportedly modeling fission weapon detonation, and understanding nebulae in interstellar space,etc.,


Fluid mechanic can also sub divide in tothree divisions.

  1. Fluid statics – study of fluid in rest

  2. Fluid kinetics – study of fluid in motion

  3. Fluid dynamics – study of fluid with effects of forces on fluid motion.


    Having problem with Fluid Dynamics Equations keep reading my upcoming posts, i will try to help you.

Bernoulli's Equation Units


Bernoulli's Equation is a special form of the Euler‘s equation derived along fluid flow stream line. So the Bernoulli’s equation’s for steady flow along a stream line of in compressible fluid is,

P/ρ + V2/2 + gz = constant(stream line) ---------> (1)

Then the equation is multiplied withdensity (ρ)

P + v2/2 + ρgz = C-------------->(2)

Where,

P– Pressure N/m2

Ρ– Density of fluid (Kg/m3)

V2 - Velocity of fluid(m6)

g- Gravity acceleration constant(9.81 m/s2)

ρV2- Kg.m3

z - Height above the arbitrary datum

c - Constant along any stream line

The constant C is remains constant along any stream line in the fluid flow but it is varies from one stream line to another stream line. C is remaining constant for all stream line where the flow is irrotational.


Bernoulli's Equation Explained


Bernoulli's equation explained the flowof fluid. When increasing the flow speed of fluid will decreasesinternal pressure and also decreases the fluid potential energy.

V2 > V1

P2


Bernoulli's equation can be consideredto be conservation of energy statement for flowing fluids. In highvelocity of fluid flow, kinetic energy must increases at theexpensive of pressure energy. Energy per unit volume before is equalto energy per unit volume after.

So the Bernoulli's equation becomes,

P1 + ½ ρV12+ ρgc1 = P2 + ½ ρV22 +ρgc2

P1, P2- Energypressure before and after respectively

½ ρV12 , ½ρV22- Kinetic energy per unit volume beforeand after respectively

ρgc1, ρgc2-Potential energy per unit volume before and after respectively


The Bernoulli’s equation can be used in different type of fluid flow then we will get the different type of Bernoulli’s equation. The simple form of Bernoulli’s equation is valid for incompressible fluid flow such as liquid flow and compressible fluid flow for gas flow.


Bernoulli's Equation Derivation


Bernoulli's equation can derived from equation of conservation of energy, which state that the sum of the mechanical energy in a fluid along a stream line is same at all points on the stream line, in a steady flow. When increasing of fluid flow occurs proportionally with an increasing in both kinetic and dynamic energy and decreasing in static pressure and potential energy.

Bernoulli's equation can derived from equation of Euler’s along the stream line.

-∂(P+ρgz)/∂s= ρa s -----------> (1)

a s= Dq/Dt = q2-q1/Dt-------> (2)

Ds/Dt = q2 + q1/2---------> (3)

Apply equation (3) to equation (1)

a s = 1/2Ds [ q22– q12 ]

= ½ D[q2]/ρs ------> (4)

When Ds = 0, the equation 4 becomes,

a s = ½ ∂q2/∂s---------> (5)

Replacing the above equation 5 in to the equation (1)

∂/∂s[ P + ρgz + ρq2/2 ]= 0

P + ρgz + ρq2/2 =Constant


Energy Equation Fluid Mechanics

(P1/w + z1 +V12/2g) + h m = (P2/w +z2 + V22/2g) + h L

h m- Energy added by machinery work such as pumps, turbines per unit weight of flowing fluid

h L- Energy loss per unit weight of flowing fluid


Bernoulli's Equation’s are approximately related with velocity, pressure and elevation and is valid for in compressible fluid with steady flow and negligible net friction flow.


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