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Fluid Mechanics Formula

This document provides formulas, units, and concepts related to fluid mechanics. It includes definitions and relationships for key terms like density, viscosity, shear stress, Reynolds number, pressure, mass flow rate, volume flow rate, velocity, Bernoulli's equation, and friction loss. Conversion factors, assumptions, and steps are outlined for using these formulas to solve various fluid mechanics problems involving things like pipes, tanks, manometers, and venturi meters.

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Kamran Zafar
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806 views3 pages

Fluid Mechanics Formula

This document provides formulas, units, and concepts related to fluid mechanics. It includes definitions and relationships for key terms like density, viscosity, shear stress, Reynolds number, pressure, mass flow rate, volume flow rate, velocity, Bernoulli's equation, and friction loss. Conversion factors, assumptions, and steps are outlined for using these formulas to solve various fluid mechanics problems involving things like pipes, tanks, manometers, and venturi meters.

Uploaded by

Kamran Zafar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Quantity Formula Units use in

problems
Density (ρ, Rho) 𝑚 Kg/m3 or
𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑣 lbs/ft3
Specific Gravity(S) S =density of liquid /density of water No units
Specific weight(ϒ, Gamma) ϒ=ρxg Newton/m3
Viscosity(µ, Mue) N. s/m2,
kg/m-s
Kinematic Viscosity(ν, Nu) 𝜇 m2/s
𝜈=
𝜌
Shear Stress(τ. Ta) Ta =Force/Area N/m2
Newton’s Law of Viscosity 𝑑𝑢 N/m2
𝜏 = 𝜇( )
Relationship between 𝑑𝑦
viscosity and shear stress Use this formula if asked to calculate shear stress given
the viscosity, velocity and distance
Reynold Number 𝐷𝑉𝜌 𝐷𝑉 No units
𝑅𝑒𝑦𝑛𝑜𝑙𝑑 𝑛𝑜 = 𝜇
or 𝜈
Pressure Pressure = Force/Area N/m2 , kg/m2
Conversion of atm, gauge Pgauge = Pabs – Patm N/m2 , kg/m2
or absolute pressure Pvac =Patm - Pabs

Pressure inside liquid Pgauge = ρgh N/m2 , kg/m2


1) If measuring gauge pressure make Patm zero

Pabs =ρ gh +Patm
(2) If measuring absolute pressure than use

N/m2 , kg/m2

N/m2 , kg/m2

When using two legged manometer, Take left


hand side above the datum line and then right
hand side above the datum line
When using multilegged manometer use the rule N/m2 , kg/m2
Go down Add
Go up Subtract

Mass flow rate Kg/sec

Volume flow rate or M3/sec


discharge

To Calculate velocity form Velocity = Discharge/Area of pipe m/sec


discharge
Calculate mass flow rate Mass flow rate =(density)(Volumetric flow rate) Kg/sec
from discharge and density M =ρQ
Continuity equation Q =ρ1A1V1 = ρ2A2V2 If density is
changing for
gases
Contiunity equation Q =A1V1 = A2V2 If density is
constant for
liquids
Bernoulli’s equation
To calculate total energy of
a system at one point
Bernoull’s equation For ideal fluid
between two point no friction or
head loss

Bernoull’s equation For real fluid


between two point with when head
losses loss and
energy loss is
there
 If a point 1 is a free surface and point (2) is a free Calculate
jet then P1 = P2 = Patm (1atm or 101kPa or 14.7 Psi unknown
or 760mm Hg depending upon the other units in velocities from
problem) Continuity eq
 if gauge pressures are used then take both
pressure as zero,
 For a large tank surface area is large so the
velocity of the surface is samll and become
zero(negligible)
If venturi meter is horizontal then take Z1= Z2 =0 Calculate
unknown from
continuity
equation

For this type of question Calculate


Take V1 = 0 (Large Tank) unknown from
P1 Tank pressure if it is closed other wise atm continuity
P2 atmpheric because it is open to atmosphere equation
V2 =0 (at point 2)
Z1 =Tank height
Z2 = jet height

For friction loss from  Calculate Reynolds number if flow is


Fanning equation laminar, use this equation to calculate
friction factor F=16/NRe
 If flow is turbulent then check type of
pipe in the problem and find ϵ from chart
 ϵ convert into meters
 Find ϵ/D and see which curve in the
graph correspond to this value
 Extend the Reynold no on x –axis upto
this line and read f from y- axis

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