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Fluid Flow


Schmidt Number
Schmidt Number

The Schmidt number is a dimensionless number that describes the ratio of momentum diffusivity to mass diffusivity that is commonly used in analysis of mass transfer systems. This article describes the Schmidt Number and typical formulations.


Episode 3 - Introduction to Hydraulics

In the third episode of the Neutrium podcast Trevor and Matt start a multi-episode arc on process hydraulics. This week they introduce the concept of pressure and discuss Bernoulli’s principal, flow regime and Reynolds number.


Cv versus Orifice Size
Cv versus Orifice Size

The pressure drop or flow rate through a valve or orifice plate is typically calculated using the a flow coefficient, Cv or orifice diameter. This article demonstrates how to convert between these two parameters when performing functions such as selecting a valve with an equivalent pressure drop to a given orifice plate.


Joule-Thomson Effect
Joule-Thomson Effect

The Joule-Thomson Effect describes the change in temperature of a gas as it experiences a rapid change in pressure from passing through a valve, orifice or nozzle. It may represent a safety hazard, or an opportunity depending on the process.


Choked Flow
Choked Flow

Choked flow is a phenomenon that limits the mass flow rate of a compressible fluid flowing through nozzles, orifices and sudden expansions. Generally speaking it is the mass flux after which a further reduction in downstream pressure will not result in an increase in mass flow rate.


Erosion Velocity for Gas-Liquid Multiphase Flow
Erosion Velocity for Gas-Liquid Multiphase Flow

The flow of a gas-liquid multiphase system may cause erosion if velocities are high. This article presents an empirical relationship for estimating whether erosion will occur in a system at a certain velocity.


Discharge Coefficient for Nozzles and Orifices
Discharge Coefficient for Nozzles and Orifices

The discharge coefficient is a dimensionless number used to characterise the flow and pressure loss behaviour of nozzles and orifices in fluid systems. Orifices and nozzles are typically used to deliberately reduce pressure, restrict flow or to measure flow rate. This article gives typical values of the discharge coefficient for common orifice and nozzle designs.


Calculation of Flow through Nozzles and Orifices
Calculation of Flow through Nozzles and Orifices

This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate.


Joukowsky Equation

The Joukowsky equation is a method of determining the surge pressures that will be experienced in a fluid piping system. When a fluid in motion is forced to either stop or change direction suddenly a pressure wave will be generated and propagated through the fluid. This pressure wave is commonly referred to as fluid hammer (also known as water hammer, surge or hydraulic shock) and typically occurs in piping systems when a valve is suddenly closed, isolating the line. The resultant surge pressures are complex to characterise but for simple systems they may be calculated using the Joukowsky equation.


Manning Characteristic Roughness
Manning Characteristic Roughness

The Manning Characteristic Roughness is used to characterise the surfaces over which water can flow in streams, channels, ditches and flumes. This article presents a reference of roughness values for many common materials of construction for channels and natural formations of streams.


Flow in Open Channels and Partially Filled Pipes
Flow in Open Channels and Partially Filled Pipes

The transport of fluid under gravity is often achieved using partially filled pipes, channels, flumes, ditches and streams. To determine the slope and elevation change required or the flow rate that is achievable one must be able to calculate the head loss and friction factor. This article provides relationships for the calculation of head loss and friction factor for fluids flowing via these conduits.


Mach Number

The Mach number is the ratio of the relative velocity of a fluid to the local speed of sound. This article provides the equation for the calculation of the Mach number and a discussion of its uses.


Speed of Sound in Fluids and Fluid in Pipes

This article provides the formulae for the calculation of speed of sound in fluids and fluid filled circular pipes. The speed of sounds is important in piping systems for the calculation of choked flow for gases and pressure transient analysis of liquid filled systems.


Comparing Volumetric Flow Rates for Equivalent Pressure Loss

Standard volumetric flow rates of a fluid are often used to describe the capacity of a vent or pressure relief device. To determine how this capacity compares for another fluid under different pressure and temperature conditions a conversion must be made on the basis of equivalent pressure loss. This article describes the method for calculating the volumetric flow rate of a gas which will give the equivalent pressure drop to another gas through a fixed restriction such as a vent.


Torricelli's Law
Torricelli's Law

This article presents Torricelli’s law, a simplified method of estimating the velocity of fluid passing through an open orifice under static pressure.


Bernoulli's Equation
Bernoulli's Equation

Bernoulli’s Principle is an important observation in fluid dynamics which states that for an inviscid flow, an increase in the velocity of the fluid results in a simultaneous decrease in pressure or a decrease in the fluid’s potential energy. This principle is often represented mathematically in the many forms of Bernoulli’s equation. This article presents some useful forms of Bernoulli’s Equations and their simplifying assumptions.


Pressure Loss in Hoses
Pressure Loss in Hoses

The Pressure loss through a hose is often approximated using coarse heuristics, but utilization of more accurate correlations increase the efficiency of pump and piping designs. This article presents more accurate methods to estimate the pressure loss in various type of hoses using multiples of the pipe length. Methods of estimating pressure loss caused by couplings, curves and coiled hose are also detailed.


Calculating Interface Volumes for Multi-product Pipelines
Calculating Interface Volumes for Multi-product Pipelines

Due to their large capital expense, pipelines are often utilized for the transfer of multiple products. During operation of these multi-product pipelines, the interface between two adjacent products extends (referred to as interface mixing), resulting in the contamination of each product. This interface is typically sent to slops collection for reprocessing or disposal at additional cost to the operator. Therefore the economics of a pipeline can often be improved through a study of product interfaces under various operational conditions to aide in the minimization of interface mixing. This article presents several empirical methods by which interface mixing can be quantified.


Estimating the Viscosity of Mixtures

For some engineering calculations, particularly in hydrocarbon processing, it is necessary to estimate the viscosity of a mixture (blend) of two or more components. This article presents the Gambill and Refutas methods, which are commonly used in petroleum refining for predicting the viscosity of oil blends.


Estimation of Pump Moment of Inertia

The moment of inertia of a pump is its resistance to changes in angular velocity as it rotates about its shaft. Knowledge of the moment of inertia of a pump, motor and associated components is typically required for transient analysis of a pumped system. This article presents methods by which pump and motor moment of inertia may be estimated.


Pressure Drop Through a Packed Bed
Pressure Drop Through a Packed Bed

As fluid flows through a packed bed it experiences a pressure loss due to friction. This article describes the use of the Carman-Kozeny and Ergun equations for the calculation of pressure drop through a randomly packed bed of spheres.


Pressure Loss from Pipe Entrances and Exits
Pressure Loss from Pipe Entrances and Exits

When a fluid moves from a tank or vessel into a pipe system or vice versa there are pressure losses. This article provides K-values for pipe entrances and exits of various geometries. These K-values may be used to determine the pressure loss from a fluid flowing through these entrances and exits.


Pressure Loss from Fittings - Expansion and Reduction in Pipe Size
Pressure Loss from Fittings - Expansion and Reduction in Pipe Size

This article provides methods to calculate the K-value (Resistance Coefficient) for determining the pressure loss cause by changes in the area of a fluid flow path. These types of pressure drops are highly dependent on the geometry and are not usually covered in simple pressure loss estimation schemes (such as a single k-value, equivalent length etc.)


Pressure Loss from Fittings - 3K Method
Pressure Loss from Fittings - 3K Method

Fittings such as elbows, tees, valves and reducers represent a significant component of the pressure loss in most pipe systems. This article details the calculation of pressure losses through pipe fittings and some minor equipment using the 3K method.


Pressure Loss from Fittings - 2K Method

Fittings such as elbows, tees, valves and reducers represent a significant component of the pressure loss in most pipe systems. This article details the calculation of pressure losses through pipe fittings and some minor equipment using the 2K method.