Summary Formula Fluid Mechanics

DCC5143 & DCC30122
– FLUID MECHANICS

FORMULA

JKA, POLITEKNIK PORT DICKSON

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Content

DCC5143 DCC30122
Topic 1- Fluid Properties Topic 1 - Fluid Characteristic

Topic 2 - Pressure Measurements Topic 2 - Measurements Of
Pressure
Topic 3 - Hydrostatic Force Topic 3 - Hydrodynamics
Topic 4 - Buoyancy & Stability Topic 4 - Flow Measurement &
Bernoulli Equation
Topic 5 - Hydrodynamics Topic 5 - Fluid Flow
Topic 6 - Flow Measurement Topic 6 Momentum Equation

Topic 7 - Fluid Flow
Topic 8 Momentum Equation

FORMULA / NO. PAGE

Topic Fluid Characteristics............................................................2
Topic Pressure Measurement.......................................................3
Topic Hydrostatic Force..................................................................3
Topic Buoyancy & Stability............................................................5
Topic Hydrodynamics......................................................................6
Topic Flow Measurement & Bernoulli Equation....................7
Topic Fluid Flow ................................................................................8
Topic Momentum Equation ...........................................................9

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TOPIC FLUID CHARACTERISTICS S = ( ) Sg = ( )
 
S = Relative density (no. unit)
= ∀ Sg = Specific gravity (no. unit)

 = Density (kg/m3)  = Density (kg/m3)
m = mass (kg)
 = volume (m3) = =

W = mg ∀

W = weight (N @ kgm/s2) ω = specific weight
m = mass (kg) W = weight (N @ kgm/s2)
g = acceleration gravity (9.81 m/s2)
 = volume (m3)

 = Density (kg/m3)
g = acceleration gravity (9.81 m/s2)

= μ=ρ

 = Dynamic viscocity (kg/ms @ Ns/m2)
Vs = specific volume (m3/kg)  = kinematic viscosity (m2/s)
 = Density (kg/m3)
 = Density (kg/m3)

Specific Weight of water,  = 9.81 kN/m3
 = @ 9.81x103 kN/m3

 = kinematic viscosity (m2/s) ρ water = 1000 kg/m3
 = Dynamic viscocity (kg/ms @ Ns/m2) s water = 1
 = Density (kg/m3)
ρ mercury = 13.6 x 103 kg/m3
s mercury = 13.6

N = kg m/s2 1 m3 = 1000 dm3
Pa = N/m2 1 m3 = 1000 liter
1 kN = 1000 N 1 liter = 1000 ml

1 MN = 106 N 1 year = 365 days
1 GN = 109 N 1 day = 24 hour
1 kg = 1000 g 1 hour = 60 minute
1 g = 1000 mg 1 hour = 3600 second

1 m = 100 cm 1 minute = 60 second
1 m = 1000 mm 1 cm = 10 mm

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TOPIC PRESSURE MEASUREMENT P = Pressure (N)
P=gh
 = density (N/m3)
g = acceleration gravity (9.81 m/s2)
h = height from datum (m)

TOPIC HYDROSTATIC FORCE FH = Horizontal force (N)
FX = FH =  g A ý Fx = Force in x-direction (N)
 = density (N/m3)
Fy = FV = W = ∀ A = area of object (m2)
ý = height from centroid (m)
̂ = ĥ = + ý FV = Vertical force (N)
ý Fy = Force in y-direction (N)
 = density (N/m3)
̂ = ĥ = + ý ∀ = volume of object (m3)
ý
ý = ĥ = height from centroid (m)
= √ + = √ + ICG = Second Moment Area (m4)
Ɵ = Inclined angle (0)
Ɵ = tan− ( ) = tan− ( )
R = Resultant force (N)
FH = Horizontal force (N)
Fx = Force in x-direction (N)
FV = Vertical force (N)
Fy = force in y-direction (N)
Ɵ = angle direction of force
FH = Horizontal force (N)
Fx = Force in x-direction (N)
FV = Vertical force (N)
Fy = Force in y-direction (N)

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Surface Surface View Area, Centroid, Second
Rectangular A ý OG Moment
(m) Area, ICG
Triangle (m2)
(m4)
Circle
Semi- circle bd d b d3
12
2

bd d b d3
23 36

 D2 D  D4
4 2 64

 r 2 4 r 0.1102 r 4
2 3

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TOPIC BUOYANCY & STABILITY FH = Horizontal force (N)
FX = FH =  g A ý Fx = Force in x-direction (N)
FY = FV = W = ∀
BG = OG – OB  = density (N/m3)
BM = A = area of object (m2)
ý = height from centroid (m)

FV = Vertical force (N)
GM = BM – BG Fy = Force in y-direction (N)

 = density (N/m3)
∀ = volume of object (m3)

BG = Difference height between centroid of
gravity & centroid of object(m)
OG = Centroid of gravity (m)
OB = Centroid of object (m)

BM = Difference height (m)
I = Moment of inertia of a horizontal
section of the body taken at the surface of
the fluid
Vd = Displaced volume of fluid (m3)

MG = Metacentric height (m)
BM = (m)
BG = (m)

Object 3d shape Surface Volume, ∀ Centroid, ý (m)
Area, A (m2) (m3)

Cuboid bd b d h h
2

Pyramid bd 1bd h 2 xh
Cylinder 3 3
 D2
4  D2 x h h
2
4

Cone  r2 1 r2 x h 2 xh
3 3

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TOPIC HYDRODYNAMICS

 Re = Reynold Number
= v = Flow velocity (m/s)
ρ = density (kg/m3)
d = inside diameter of pipe section (m)
µ = dynamic viscosity of the fluid (kg/ms) @ (Ns/m2)
=   = kinematics viscosity of the fluid (m2/s)

i. Laminar flow when Re < 2300
ii. Transition flow when 2300 < Re < 4000
iii. Turbulent flow when Re > 4000

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TOPIC FLOW MEASUREMENT & BERNOULLI EQUATION

Contuinity equation

Q=AV Q = flowrate (m3/s)

A = area of pipe (m2)

v = velocity (m/s)

Bernoulli equation

H = + + z H = total energy (m)
 P = Pressure head (N/m2)
 = density (N/m3)

v = velocity (m/s)

z = height from datum (m)

Q = √ Venturimeter

√( − )

H = ( ) . x − Q = Flowrate (m3/s)
A1 = Main area (before contraction) (m2)
A2 = Neck area (contraction) (m2)
H = Height of venturymeter (m)
= ( ) . x −  Sgmercury = Specific gravity of mercury (13.6)
Sgfluid = Specific gravity of fluid
 mercury = Density of mercury (13600 N/m3)

Q =√( − )

Q = Cd A1 √( − ) fluid = Density of fluid (N/m3)
x = level of mercury in two differents arms (m)

m = Orifice



Q = Flowrate (m3/s)

Qact = Cd Ao √ HL = Head losses (m)
v = Velocity (m/s)

Vact = Cv √ Cd = Discharge coefficient

Cc = = Cv = Velocity coefficient
Cc = Contraction coefficient

A1 = Area before enlargement (m2)
Q = . √ [ / − / ] A2 = Area enlargement (m2)

Q = . √ / h1 = Height of level water before flow (m)
h2 = Height of level water after flow (m)

H = Difference height of level water (m)

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TOPIC FLUID FLOW

HL= 4 f L v2 Major Losses
2gd HL = Head losses (m)

HL= f L Q2 f = friction coefficient
3 d5
L = pipe length (m)
hL = .
v = velocity (m/s)

hL = ( − ) d = pipe diameter (m)
Q = flowrate (m3/s)
Minor losses ( Entrance / inlet loss )
hL = ( HL = Head losses (m)

− ) v = velocity (m/s)
Minor losses ( suddenly contraction)
Cc = HL = Head losses (m)

v1 = velocity before contraction (m/s)

hL = v2 = velocity contraction (m/s)
Minor losses ( suddenly enlargement )
HL = Head losses (m)
hL =
v = velocity (m/s)

HL = Cc = contraction coefficient
A1 = Area before enlargement (m2)
A2 = Area enlargement (m2)
HL= 4 f L v2 Minor losses ( bend loss )
2gd HL = Head losses (m)

v = velocity (m/s)

F = Head loss at bend coefficient (given)
Minor losses ( exit / outlet loss )
HL = Head losses (m)

v = velocity (m/s)
Hagen-Poiseuille formula
 = dynamic viscosity (Ns/m2)

L = length of pipe (m)

v = velocity (m/s)
 = density (N/m3)

d = diameter of pipe (m)
Darcy-Weisbach formula
HL = Head losses (m)

f = friction coefficient

L = pipe length (m)

v = velocity (m/s)

d = pipe diameter (m)
Q = flowrate (m3/s)

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TOPIC MOMENTUM EQUATION Fixed plate held vertical to the jet
F = ρ A V2 F = Force (N)
 = Density (N/m3)
F = ρ A V 2 sin θ A = Area of pipe (m2)
v = velocity jet (m/s)
F=ρA(V–u)2 Fixed plate held inclined to the jet
Ɵ = Inclined angle from x-axis (0)
F = ρ A ( V – u ) 2 sin θ
F =  ( A x ( V – U / sin  )) (V sin  – U) Moving plate held vertical to the
Fx = ρ A V 2 ( 1 + cos θ) jet
Fy = ρ A V 2 sin θ Ɵ = Inclined angle from x-axis (0)
Fx = ρ A ( V – u ) 2 (1 + cos θ) v = velocity jet (m/s)
Fy = ρ A ( V – u ) 2 sin θ u = velocity after jet (m/s)
= √ + Moving plate held inclined to the
Ɵ = tan− ( ) jet
Ɵ = Inclined angle from x-axis (0)
v = velocity jet (m/s)
u = velocity after jet (m/s)
Fixed curved vane
Ɵ = Inclined angle from x-axis (0)
v = velocity jet (m/s)

Moving curved vane
Ɵ = Inclined angle from x-axis (0)
v = velocity jet (m/s)
u = velocity after jet (m/s)
R = Resultant force (N)
Fx = Force in x-direction (N)
Fy = force in y-direction (N)
Ɵ = angle direction of force
Fx = Force in x-direction (N)
Fy = Force in y-direction (N)

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