Equation Sheet for Exam 1 PDF

Preview

Summary

Download Equation Sheet for Exam 1 PDF

Description

Equation Sheet for Exam #1 Specific weight: 𝛾 = 𝜌𝑔. Specific gravity 𝑆𝐺 = Kinematic viscosity: 𝜈 =

𝜇 𝜌

𝜌 𝜌𝐻2 𝑂@4𝑜𝐶

.

(𝜇 is dynamic viscosity).

Ideal gas law: 𝑝 = 𝜌𝑅𝑇 Shear force on a surface A of unidirectional flows of u=u(y):𝐹 = 𝜏𝐴 ; shear stress 𝜏 = 𝜇 Bulk modulus: 𝐸𝑣 = −

𝑑𝑝 𝑑𝑣 𝑣

=

𝑑𝑢 𝑑𝑦

𝑑𝑝 𝑑𝜌 𝜌

Speed of sound in an ideal gas:c = √kRT 4𝜎

2𝜎

Surface tension: ∆𝑝𝑏𝑢𝑏𝑏𝑙𝑒 = 𝑅 , ∆𝑝𝑑𝑟𝑜𝑝𝑙𝑒𝑡 = 𝑅 ; Capillary rise: ℎ = length of an solid object in contact with a liquid surface) Pressure gradient:

𝑑𝑃 𝑑𝑧

2𝜎 𝑐𝑜𝑠𝜃 𝛾𝑅

. 𝐹 = 𝜎𝐿 (L is the

= −𝜌𝑔 (assuming g is in the opposite of +z direction)

Pressure variation in a stationary incompressible fluid: pdown = pup + 𝛾|Δ𝑧|. Hydrostatic force on a plane surface: FR = PC A; yR = yC +

γIxc sin θ PC A

. ; xR = xC +

If patm is applied on both sides of the plane, FR = γ hC A, yR = yc +

Ixc , yC A

γIxyc sin θ

xR = xc +

PC A Ixyc yC A

Unit Conversion 1 m = 3.28 ft; 1 ft = 12 in; 1 in = 0.0254 m or 2.53 cm , 1 liter = 10-3m3; 1 gallon = 0.1337 ft3; 1 Pstd = 14.686 psia = 101.3 kPa, 1 psi = 1 lbf/in2 = 144 lbf/ft2 = 144 psf = 6.894 kPa 1 lbf = 4.4482 N ; 1 lbm = 0.45359 kg, g=9.81 m/s2=32.2 ft/s2 Fluid Properties (at 20C and 1 atm) 1000kg/m3

Water ρ = = 1.94 slug/ft3 , γ = 62.43 lb/ft 3 μ = 10−3kg/(m. s). Air ρ = 1.22 kg/m3, μ = 1.8 × 10−5 kg/(m. s). Air gas constant R=287J/(kg.K)....