• • • Article No. VK-PHY15

# PHY15 Fluid Mechanics

Demonstration of fundamental fluid laws during flow measurements using the ultrasonic Doppler effect

Flow measurements according to the ultrasonic Doppler method are used to demonstrate fundamental laws governing the flow of liquids in pipes and their dependence on the flow velocity and the pipe geometry.

Keywords: Laminar and turbulent flow, continuity equation, Reynolds number, Bernoulli’s equation, Hagen-Poiseuille equation, flow velocity, flow resistance, pressure scales, static and dynamic pressure, viscosity

With this experiment structure, the Doppler frequency shift can be measured for different pump speeds at measurement sections with different pipe diameters. At the same time, the corresponding pressure drops can be measured by means of standpipes. In this way, it is possible to obtain clear evidence of the laws that apply to a liquid with laminar flow. From the flow velocities determined according to the Doppler method, the pipe geometries and the measured pressure drops, it is possible to determine flow rates, flow resistances and the dynamic viscosity of the Doppler liquid by formulaic application of the continuity equation, Bernoulli’s equation and the Hagen-Poiseuille equation. By calculating the Reynolds numbers for the different flow velocities and pipe diameters, it is possible to check whether stationary laminar flow states were prevalent during the measurements.

From the flow rates measured and the specific crosssectional areas, the corresponding flow can be calculated. This is nearly equivalent in this experimental setup for all pipe diameters for the same settings of the centrifugal pump, thus satisfying the continuity equation. As a further result, the diagram below shows the flow resistance R determined for different pipe diameters and different flows. This shows the strong dependence on the pipe radius r to be expected from the Hagen-Poiseuille equation: R ~ 1/r4.

 PHY13 Ultrasonic Doppler effect IND05 Doppler flow measurement MED03 Basics of Doppler sonography MED05 Vascular ultrasound (angiology) MED06 Peripheral Doppler blood pressure measurement