This document contains study guide information for a fluid mechanics course. It summarizes key concepts from the first two chapters, including definitions of density, specific weight, specific gravity, viscosity, shear stress, shear strain, and the ideal gas law. It also covers fluid pressure, Pascal's law, hydrostatic pressure equations, atmospheric pressure, gauge pressure, manometer equations, and calculations of hydrostatic forces on surfaces immersed in fluids.

1. Dennis Albert June 4, 2018
www.dennisusa.com
Fluid Mechanics Study Guide
Chapter 1. Fundamental concepts
Density:  =
𝑚
𝑉
Specific weight:  =
𝑊
𝑉
 = g
Specific gravity: SG =

(ref)
=

(ref)
Ideal gas law: p = RT (R=286.9J/kg.K, J=N.m)
Bulk modulus (a measure of the amount by which a fluid offers a resistance to compression):
E = -
𝑑𝑃
𝑑𝑉/𝑉
Viscosity: mass/(time*length)
Shear stress (the motion which is a consequence of the shearing effect within the fluid caused
by the plate):  =
𝑑𝐹
𝑑𝐴
 = *
𝑑𝑢
𝑑𝑦
Shar strain (the shear stress causes each element to deform into shape of a parallelogram, the
resulting deformation is defined by its shear strain, specified by the small angle ):
 = tan  =
x
y
Newton’s law of viscosity:  = *
𝑑𝑢
𝑑𝑦

2. Dennis Albert June 4, 2018
www.dennisusa.com
Chapter 2 Fluid Statics
Pressure: p =
𝒅𝑭
𝒅𝑨
Pressure can have units of Pa = N/m2, psf = lbf/ft2, psi = lbf/in2
P = F/A = ghA = hA
Pascal’s Law: Pressure at a point in a fluid at rest, or in motion, is independent of direction, as
long as there are no shearing stress present.
Pressure of fluid at rest: dP = -  *dZ Z = elevation
𝑑𝑃
𝑑𝑍
= − 
Incompressible fluid (constant fluid density):
𝑑𝑃
𝑑𝑍
= − 
P1 – P2 = −  (Z2 – Z1)
P1 – P2 =  ∗ h, h=Z2-Z1
Compressible fluid (fluid density changes with temperature and pressure):
P2 = P1exp[- 𝑔(𝑍2−𝑍1)
𝑅𝑇0
]
Atmospheric pressure (measured by barometer): Patm = h + Pvapor
Gauge pressure (measured by manometer): p = h + p0
Manometer rule: p1 + *hdown - *hup = p2
Hydrostatic force on a plane surface: FR = p*A (FR: resultant force)
FR = hc *A (hc is the vertical distance from the fluid surface to the centroid of the area)
Location of the resultant force on x axis: yR = IXC/ycA + yc
Location of the resultant force on y axis: xR = IXC/xcA + xc