## Illustration 15.3: Ideal and Viscous Fluid Flow

Bernoulli's equation describes the conservation of energy in an ideal fluid system such as the one shown in this animation (position is given in tenths of meters and pressure is given in pascals). Restart. The vertical tubes are open to the atmosphere. Notice that the water level is lower to the right, indicating a lower pressure. Why is the pressure lower in the narrower tube? Notice also that the pressure only changes when going from a wider to a narrower tube. The pressure indicator measures the gauge pressure, not the absolute pressure (gauge pressure is pressure above atmospheric pressure). When there is viscosity (that is the fluid sticks together a bit so there is some friction), but still a smooth (laminar) flow, the pressure drops along the length of a pipe. Try it. For viscous flow, notice that, to get the same volume per unit time (Av = volume/time, where A is the cross-sectional area and v is the speed of the fluid flow), the pressure drops more in the narrower tube than in the wider tube. The equation governing the flow is Poiseulle's equation, Av = πR4ΔP/8ηL, where R is the radius of the tube, L is the length of the tube, ΔP is the pressure difference and η is the viscosity of the fluid.

Note: The format of the pressure is written in shorthand. For example, atmospheric pressure, 1.01 x 105 Pa, is written as 1.01e+005.

Illustration authored by Anne J. Cox.

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