![]() The dynamic viscosity of water varies from about 1.8 centipoise at \(0 \circ \) C to about 0.3 centipoise at \(100 \circ \)C. If, for a transverse velocity gradient of 1 m s −1 per cm, the tangential force per unit area is 1 N m −2, the dynamic viscosity is one decapoise. The SI (MKS) unit is the decapoise (also spelled dekapoise), though the SI unit the pascal second (Pa s), which is dimensionally correct, is also seen. That is to say, if, for a transverse velocity gradient of 1 cm s −1 per cm, the tangential force per unit area is 1 dyne cm −2, the dynamic viscosity is one poise. The unit is named after a nineteenth century French doctor, Jean Poiseuille, who was interested in blood pressure and hence in the rate of flow of liquids through tubes. The abbreviation for the unit is P – though it would be well to define it if you use it, since not everyone will recognize it. The CGS unit of dynamic viscosity is the poise. The dimensions of dynamic viscosity are ML −1T −1. The ratio of the tangential force per unit area to the transverse velocity gradient is called the coefficient of dynamic viscosity, for which the usual symbol is \( \eta \). As a consequence of the transverse velocity gradient, the liquid below the dashed line will be dragged forward by the tangential force of the faster liquid above it, and the liquid above the dashed line will be dragged backward by the tangential force of the more sluggish liquid below it. There will be a transverse velocity gradient \(dv/dz\), with the liquid stationary at the river bottom, and the speed becoming faster as we ascend from the bottom. ![]() \)Ĭonsider a river flowing over a smooth bed, as in Figure XX.9.
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