Fluid Mechanics Equation Sheet Full

Fluid Mechanics Equation and Data Sheet 1. Hydrostatics: 1.1 General Equation


  
 For a constant density fluid:

    

where  = pressure at Point 1 (Pa)  = pressure at Point 2 (Pa)  = fluid density (kg.m-3)  = elevation of Point 1 relative to a datum (m)  = elevation of Point 2 relative to the same datum (m)  = gravitational acceleration (m.s-2) 1.2 Absolute and Gauge Pressures

      where  (Pa) and   (Pa) are the gauge and atmospheric pressures, respectively. 2. Control Volume Analysis: 2.1 Mass Balance

  

where  = mass flow rate at Section 1 (kg.s-1)  = mass flow rate at Section 2 (kg.s-1) [P.T.O.]

2.2 Momentum Balance

Σ       where  = forces (N), e.g. gravity, pressure, friction, external…  = velocity vector at Section 1 (m.s-1)  = velocity vector at Section 2 (m.s-1) 3. Bernoulli’s Equation: Between Points 1 and 2 along the same streamline:

1 1       

2 2 where  = pressure at Point 1 (Pa)  = pressure at Point 2 (Pa)  = fluid density (kg.m-3)  = speed at Point 1 (m.s-1)  = speed at Point 2 (m.s-1)  = elevation at Point 1 (m)  = elevation at Point 2 (m)  = gravitational acceleration (m.s-2) 4. Frictional Losses in Pipes: Between Point 1 (upstream) and Point 2 (downstream) in the pipe:

1             ;   2



4"  #

with

$ &#

 ; % % 4 [P.T.O.]

where  = pressure at Point 1 (Pa)  = pressure at Point 2 (Pa)  = fluid density (kg.m-3)  = elevation at Point 1 (m)  = elevation at Point 2 (m)  = gravitational acceleration (m.s-2)  = the average flow velocity in the pipe $ = volumetric flowrate (m3.s-1) % = cross-sectional flow area (m2) " = pipe length (m) # = pipe diameter (m) = Fanning friction factor The Fanning friction factor

is given by:

16 ; for Laminar 2low () 1 1.254 : ⁄#  1.74 ln 8 ? ; for Turbulent 2low 3.708 ()5 5 

with : = absolute roughness (m) and the Reynolds number for pipe flow is defined as:

() 

# E

where E = fluid dynamic viscosity (kg.m-1.s-1) 5. Compressible Flow through Nozzles: 5.1 Compressible Bernoulli Equation Between Points 1 and 2 along the same streamline: [P.T.O.]

1 1 F   F 

2 2 where G = specific (per unit mass) enthalpy at Point 1 (J.kg-1) G = specific (per unit mass) enthalpy at Point 2 (J.kg-1)  = speed at Point 1 (m.s-1)  = speed at Point 2 (m.s-1) with the specific heat capacity at constant pressure for a perfect gas, given by:

HI  

J K  J L

where J = ratio of specific heat capacities K = 8.314 J.mol-1.K-1, the Universal Gas Constant L = molar mass (g.mol-1) 5.2 Isentropic Prefect Gas Processes J

I N J O JP     IM NM OM and

H  5JKO⁄L where I = pressure (Pa) N = density (kg.m-3) O = absolute temperature (K) ‘M’ = subscript denoting stagnation conditions J = ratio of specific heat capacities K = 8.314 J.mol-1.K-1, the Universal Gas Constant L = molar mass of fluid (kg.kmol-1) H = speed of sound (m.s-1) [P.T.O.]

6. Compressible Flow in a Pipe:

    2

(Q

 2" S Tln    U 

R #

where I = pressure at pipe inlet (Pa) I = pressure at pipe outlet (Pa) K = 8.314 J.mol-1.K-1, the Universal Gas Constant O = absolute temperature (K) L = molar mass of fluid (kg.kmol-1) V = mass flux (kg.s-1.m-2) W = friction factor X = pipe length (m) Y = pipe diameter (m) [END]