Horizontal Cylinderical Tanks

Tanks are used for the storage fluids in many chemical process industries. For a horizontal cylinderical tank, the two ends (heads) of the vessels is usually both flat, dished, elliptical or hemispherical. It is commonly required to estimate the quantity of fluid in a tank when it is partly filled with fluid, and only fluid level is known. This partial volume is made up of the volume in the cylinderical shell plus the volumes in the two heads. The partial volumes can be estimated by the equations below:
Partial volume of horizontal cylinder:
    = {r²cos^-1[(r - h)/r] - (r - h)(2rh - h²)^0.5}L
Partial volume of dished heads:
    = 0.215483*h²(1.5d - h)
Partial volume of elliptical heads:
    = 0.5236*h²(1.5d - h)
Partial volume of hemispherical heads:
    = 1.0472*h²(1.5d - h)
where
     L = side length of the cylinder shell
     d = internal diameter of the cylinder
     r = radius of the cylinder = d/2
     h = height of liquid in the cylinder
All volume equations give fluid volumes in cubic units from tank dimensions in consistent linear units.

Sizing Of Orifice For Liquid Flow

The orifice meter is a device for measuring the rate of flow of liquid and gas through a pipe. Typically, it consists of a flat circular plate which has a circular sharp-edged hole called orifice, which is concentric with the pipe. In chemical process design, an orifice is usually sized for known flowrate and presure drop. For liquid flow, the commonly applied equations are:

     
where
     d = orifice diameter, inch
     C_D = maximum allowable vapor velocity ≈ 0.62
     D = pipe inner diameter, inch
     Δp = pressure differential, psia
     W = full-scale upstream mass flow rate, lb/s
     ρ= upstream liquid density, lb/ft³

REYNOLDS NUMBER AND FRICTION FACTORS

Flow Through Circular Pipe

The Reynolds Number (Re), is a dimensionless parameter for characterizing fluid flow. It is the criterion used to determine whether flow is Laminar, Critical (transitional) or Turbulent. Usually for laminar flow Re < 2100, for critical flow Re is between 2100 and 4000, while turbulent flow prevails for Re > 4000.

The Darcy friction factor is a Reynold number-dependent factor used in the calculation of the pressure loss due to pipe roughness. Friction factor is commonly calculated via the implicit Colebrook-White equation and more recently by explicit equations by Churchill, and by Swamee & Jain. Colebrook-White and the Swamee-Jain equations were designed for the turbulent flow regime, but will be used here also for the critical regime. Churchill's equation spans the entire range from laminar to turbulent. The Fanning factor and the Transmission factor are derivatives of the Darcy friction factor. The relevant equations are given below:
    Reynolds Number R_e=VD/ν

     
   Fanning friction factor ƒ_f=ƒ_d/4
   Transmission factor F =2/√ƒ_d
where
     R_e = Reynolds Number
     V = average flow velocity
     ν = kinetic viscosity, centistokes
     D = pipe inside diameter
     ε = absolute internal pipe roughness
     ƒ = friction factor
     ƒ_d = Darcy friction factor
     ƒ_f = Fanning friction factor
     F = Transmission factor