If the velocity vector at the pipe wall is zero, the maximum velocity occurring in the pipe can be worked out mathematically.įigure 2: Sample Newtonian Fluid Velocity Profile For steady flow in a pipe of radius 'R' containing a smaller cylindrical element of liquid radius 'r,' a shear force develops equal and opposite to the cylindrical water element pressure.Ĭonsider a pipe of radius 'R' that contains a smaller cylindrical element of liquid of radius 'r.' See Figure 2.Īssuming the cylindrical element of fluid is moving uniformly through the pipe, at constant velocity, the shearing force on the pipe wall is equal to the pressure force of the liquid moving through. It is this boundary condition that distorts a Newtonian fluid's velocity profile. In fact, the boundary conditions placed on the stationary pipe wall demand that the fluid in direct contact with the pipe walls have zero velocity (or at least that is what is assumed in the calculations within this article). The flow of a Newtonian fluid will exhibit a 'sticking' effect on the walls of the pipe. The viscosity of a Newtonian fluid is dependent only on temperature, but not on shear rate and time. Distortions can occur for homogeneous Newtonian fluids for a number of reasons. However, every liquid has some measure of viscosity therefore, the velocity profile becomes distorted from this 'ideal case scenario.'Įxamples of Newtonian fluids include water, milk, sugar solutions and mineral oils. That is, the fluid velocity at the pipe walls is equal to the fluid velocity at the pipe center and at all points in-between. In this example, the velocity gradient is constant and equal across the entire cross-section. The cross-sectional view shown in Figure 1 illustrates a hypothetical situation in which the fluid has zero viscosity. The vertical sheet of fluid moves forward at velocity V. If a vertical cut were made through the center of the pipe to remove the front half of the pipe, it would be easy to see how 'nicely behaved' fluid flow develops.įigure 1: Zero Liquid Viscosity In the hypothetical situation shown here, the liquid viscosity is zero, and the velocity profile is a straight line. Imagine a horizontal pipe a few feet in front of you at about eye level. With this background, we will then look at how these influence quantities factor into flowmeter performance and what can be done to minimize their effect. This article will discuss the first of four major influence quantities that affect flowmeter accuracy and performance: velocity-profile deviations, non-homogenous flow, pulsating flow, and cavitation. If deviations from these conditions exist, accuracy and/or repeatability will degrade. Sounds silly right? But these are the hypothetical conditions upon which flowmeter accuracies are based. A world in which pipes always contain fully developed turbulent flow and pipe bends and obstructions are non-existent. Reprinted from Chemical Processing magazineĬlose your eyes and imagine a world in which all fluids flowing down pipes are perfectly homogeneous, having no disturbances or eddies in the flow stream. Selecting the right flowmeter for the liquid HALO® Chromatography Columns and Consumables+. Sartorius laboratory instruments, consumables and services PerkinElmer - Innovating for a Healthier World Lab Thermometers & Temperature Measurement EquipmentĪgilent Chemistries and Supplies Portfolio Quality Products from Sheldon Manufacturing Life Science Research Solutions, Products, and Resources

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Twist in time laminar flow