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Fluid Mechanics

Units

There are several systems of units used, we will talk about the common two

1- SI :- International System of Units

2- US :- United States System of Units

General Units

General Units

Equal from the Base Unit

1000,000,000 Giga

1000,000 Mega

1000 Kilo

100 Hecto

10 Deca

0.1

Deci

0.01

Centi

0.001

Milli

0.000 001 Micro

0.000 000 001 Nano

Basic Parameter

Parameter

Length(L)

Time(t)

Mass(m)

Temperature(T)

SI Units

1m=100cm=1000m m

1hr=60min

1min=60sec

1kg=1000g

US Units

1ft=12in

The Same

1lb=16oz

K=273.15+C F=(K*9/5)-459.67

Convert

1m=3.28ft

1in=2.54cm

1kg=2.2lb

F=(C*9/5)+32

C=(F-32)*5/9

Assistance

Area unit (A)= Square Length units

Volume unit (V) = Cubic Length units

Simple Equation

Velocity (v)= L/t

Acceleration (a)= L/t^2

Important Equations

Density (ρ) = m/V

Force (f) = m*a = P*A (N=0.10197Kgf)

Pressure (P) = F/A = ρ*g*h

(1 bar =100,000 Pa)(1 psi = 6894.8Pa)

Work (W) = F*L (j)

Power (E) = F*V (w)

Fluid Properties

The fluid properties depend on the type of fluid , fluid temperature and fluid pressure.

The most Important properties for as are the Density (ρ) and the Viscosity (µ)

Viscosity

What is the viscosity? The viscosity is the fluid resistance to flow.

It measured by force the fluid in a known tube and measure the flow rate

(µ) unit is Kg/(m*s) or Pa*s or poise

Poise=0.1 Pa*s

Mass Conversation

We use this equation for 1-D laminar flow

A1*V1=A2*V2

Energy Conversation

(P1/ρ*g)+(v1/2*g)+(z1)+(E/mʹ*g)=

(P2/ρ*g)+(v2/2*g)+z2

Examples

As we see in the Example there is a pump to take water from Nile to 8 m higher.

Given information:-

Z2 = 8m

Vʹ = 15 l/s

D1 = 154 mm

D2 = 102 mm

ρ = 1000 Kg/mᶾ

Required:-

1- v1 and v2

2- The Pump Power

Solution

A1*v1 = A2*v2 = Vʹ = 0.015 m^3/s

A1 = (Π/4)*D1^2 = 0.0186 m^2

A2=(Π/4)*D2^2 = 0.00816 m^2 v1 = Vʹ/A2 = 0.81 m/s v2 = Vʹ/A1 = 1.84 m/s

(P1/ρ*g)+(v1/2*g)+(z1)+(E/mʹ*g) =

(P2/ρ*g)+(v2/2*g)+z2

P1=P2=Pa v1 = 0 z2-z1 = 8m mʹ = ρ*Vʹ = 1000*0.015 = 15 Kg/s

E = mʹ*g*(v2^2/2*g + (z2-z1)) = 1203 w

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