3.3 Path line

Fig 7.3 Path Lines

• Path line refers to a path followed by a fluid particle over a period of time and show direction of velocity

•  Two path lines can intersect each other as or a single path line can form a loop as different particles or even same particle can arrive at the same point at different instants of time.

• While stream lines shows an imaginary curve in a flow field for a fixed instant of time, tangent to which gives the instantaneous velocity at that point.

• Two stream lines can never intersect each other, as the instantaneous velocity vector at any given point is unique.

Next flow rate and mean velocity http://fluidbloggroup3.blogspot.com/2014/05/fluid-34-35.html

3.1 Introduction

Ø Fluid Mechanics is the branch of science that studies the dynamic properties (e.g. motion) of fluids

Ø The motion of fluids can be characterized by a continuum description (differential eqns.)

Ø Fluid movement transfers mass, momentum and energy in the flow.

Ø We are studying fluid mechanics because fluid are an important part of many problems that a civil engineering considers.

1.     Water resource engineering ( water deliver to consumer  and disposal after use)

2.     Water power engineering ( water use to generate electirc power,flood control , drainage)

3.     Structural engineering (wind water creates force on structure)

•      So we need to find a way to investigate the motion and nature phenomena of fluid

•      Use mathematic to model the fluid

•      Most fundamental of Approximation is assumption of continuum

•      Let fluid and flow properties such as mass density, pressure,  velocity

•      Possible to integration and differentiation these function

•      Application of equation and theory~~should have Good agreement between theory and experiment 






Next type of flow http://fluidbloggroup3.blogspot.com/2014/05/fluid-31-33-type-of-flow.html

3.7 Momentum of Fluid Mechanics

According to Newton’s Second Law of Motion, the momentum can define as 

                             

 

Fluid contain in tube ABCD move to A’B’C’D’ after time changing, dt and since momentum = mass × velocity

AA’B’B = ρ₁A₁v₁ dt× v₁

 = ρ₁A₁v₁² dt

CC’D’D = ρ₂A₂v₂dt× v₂

= ρ₂A₂v₂² dt

Momentum changing in time = ρ₂A₂v₂² dt - ρ₁A₁v₁² dt

By dividing dt,

Momentum rate = ρ₂A₂v₂² - ρ₁A₁v₁²

In any steady flow, ρ₁A₁v₁ = ρ₂A₂v₂ = m, thus, momentum rate is

• Momentum rate = m(v₂ - v₁)

Therefore, Force, F is given by

•  Force, F = m(v₂ - v₁)

For any steady flow in three dimension equations can be express as:

The application of Momentum Equations

a)    Structure Open to Atmosphere

b)    Force of Pressure Conduits and Bend

c)     Force of A Stationary Vane or Blade

d)    Force of Nozzle 

Example

A water jet strikes on a vane at 150⁰. If water flows and velocity are 0.68 kg/s and  24 m/s respectively, calculate the resultant force at stationary vane ?

Enjoy some video, you may more easily to understand what is talking about this subtopic.