Fluid Momentum Flux Equation and Calculator

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Fluid Momentum Flux Equation and Calculator

Fluids Dynamics and Engineering
Hydraulic and Pneumatic Knowledge

Momentum Flux is the rate of change of momentum flowing through unit area.

Mass flow rate of a system is a measure of the mass of fluid passing a point in the system per unit time. The mass flow rate is related to the volumetric flow rate.

Eq. 1
Calculation of momentum Flux
τ_xy = - µ · ( Δv_x / Δ_y )

This equation, which states that the shearing force per unit area is proportional to the negative of the velocity gradient, is often called Newton's law of viscosity. Actually we should not refer to Eq. 1 as a "law," since Newton suggested it as an empiricism the simplest proposal that could be made for relating the stress and the velocity gradient.

Where:

µ = Fluid Viscosity (lb_f · s/ft²)
Δv_x = Change in Velocity in the x-direction (ft/s)
Δ_y = Plate Separation in the y-direction (ft)
τ_xy = Momentum Flux (lb_f/ft²)

Summary of Units for Quantities

	SI	c.g.s	British
τ_xy	Pa	dyn/cm²	poundals/ft²
v_x	m/s	cm/s	ft/s
y	m	cm	ft
µ	Pa · s	gm/cm · s = poise	lb_m/ft · s
v	m²/s	cm²/s	ft²/s

Viscosity of Water and Air at 1 atm Pressure

Temperature T ("C)	Water (liq.)^a		Air^b
Temperature T ("C)	Viscosity p (mPa s)	Kinematic viscosity v (cm²/s)	Viscosity p (mPa. s)	Kinematic viscosity v (cm²/s)
0	1.787	0.01 787	0.01716
20	1.0019	0.010037	0.01813
40	0.6530	0.006581	0.01908
60	0.4665	0.004744	0.01999
80	0.3548	0.003651	0.02087
100	0.2821	0.002944	0.02173

^a Calculated from the results of R. C. Hardy and R. L. Cottington, J. Research Nut. Bur. Standards, 42, 573-578 (1949); and J. F. Swidells, J. R. Coe, Jr., and T. B. Godfrey, J. Research Naf. Bur. Standards, 48,l-31 (1952).
^b Calculated from "Tables of Thermal Properties of Gases," National Bureau of Standards Circular 464 (1955), Chapter 2.

Viscosities of Some Gases and Liquids at Atmospheric Pressure

Source:

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley & Sons, Chapter: 1, Page: 15.