Interacting Tank Reservoirs
Samir Khan
Adept Scientific plc
Introduction
This worksheet models the draining of liquid from one tank into into another tank through a connecting pipe. The flow is opposed by pipe friction, and the level of liquid in each tank oscillates to an equilibrium. Differential equations that describe the dynamic change in liquid height in each tank and a momentum balance are solved numerically.
Physical Parameters
Cross-sectional area of tanks
Diameter, length, and relative roughness of pipe
Density and viscosity of liquid
Gravitational constant
Governing Equations and Their Solution
Friction Factor
The following procedure gives the friction factor as a function of the flowrate. If the flowrate is turbulent (i.e., the Reynolds number is greater than 2300), it uses the Swamee and Jain approximation to the Colebrook equation, or the standard equation for the friction factor in laminar flow otherwise.
Differential Equations
The rate of change of liquid height in Tank 1
The rate of change of liquid height in Tank 2
A momentum balance
Initial Conditions
Numerical Solution of Governing Equations
Results
References
Chemical Engineering Dynamics, Ingham et al., Wiley-VCH, 2000.
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