E l e m e n t a r y F l u i d M e c h a n i c s

By Rasikh Tariq

1Department of Mechanical Engineering - Mohammad Ali Jinnah University, Islamabad Campus

Concept of Streamline & Normal

The lines that are tangent to the velocity Vectors throughout the flow field.

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Balancing Newton’s 2nd Law

Assumptions

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Inviscid Fluid Analysis Steady-Flow Analysis

Inviscid Fluid Analysis:- The Fluid is assumed to have ZERO Viscosity.

Steady Flow Analysis:-Fluid properties (Either Intensive or Extensive) that are

independent of TIME.

Balancing Newton’s 2nd Law

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Balancing Newton’s Law Normal to Streamline

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Balancing Newton’s Law Normal to Streamline

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The equation tells us Pressure Variation along the path Normal to Streamline. i.e Depending On the Path.

Assumptions:- Inviscid Flow Steady-flow Fluid Analysis Valid for Fluids that are only experiencing Pressure & Weight.

Balancing Newton’s 2nd Law Along the Streamline

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Pressure Variation Along the Streamline i.e. Path Function

Across 2 different Points i.e. Point Function

Assumptions:- Invscid Flow Analysis Steady Flow Analysis

is also Bernoulli's Equation.

Further Assumption – Bernoulli's Equation

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For Incompressible Flow i.e. Density is constant along the Streamline

is also Bernoulli's Equation.

Assumptions:- Inviscid Flow Analysis Steady Flow Analysis Incompressible Fluid Analysis Only applicable along the Streamline

Restrictions:- Rotational Effects Concept of Vorticity No External Mechanical Devices

(Pumps & Turbines)

Effects of Compressibility

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For Incompressible Flow i.e. Density is constant along the Streamline

Assumptions:- Compressible Isentropic (Internally Reversible & Adiabatic Process or constant

Entropy) Steady Flow

k=Where

Concept of Stagnation Point

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Fluid Velocity is ZERO at Stagnation Point.

Applying Bernoulli's Equation

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Stagnation Point

Applying Bernoulli's Equation- Free Jet

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d

1

2

h

By Balancing Bernoulli's Equation, we get.

Applying Bernoulli's Equation- Free Jet

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Co-efficient of Contraction

Applying Bernoulli's Equation- Free Jet

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Co-efficient of Contraction

Applying Bernoulli's Equation- Free Jet

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Co-efficient of Contraction

Applying Bernoulli's Equation- Free Jet

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Co-efficient of Contraction

Flow Rate Measurement – Closed Channel

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Balancing Bernoulli's Eq

0 0

Further Simplifying using

We come up with

Flow Rate Measurement – Closed Channel

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Open Channel (Lower Stream)

Sluice Gate

And

We come up to the Result

Note : But make sure, Never forget all the Assumptions

Flow Rate Measurement – Closed Channel

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Open Channel (Upper Stream)

Weir

Flow Rate Measurement – Closed Channel

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Open Channel (Upper Stream)

Weir

And

We come up to the Result

Note : But make sure, Never forget all the Assumptions

Thank you

22Department of Mechanical Engineering - Mohammad Ali Jinnah University, Islamabad Campus