The Physics Teacher, Vol. 41, No. 6, pp. 345–350, September 2003
©2003 American Association of Physics Teachers. All rights reserved.
Previous section: BODY OF ARTICLE
Next section: Exponential Decay Experiment
Title Page

Streamline Fluid Flow

Laminar flow of a viscous fluid through a horizontal capillary tube is described by Poiseuille's equation,3 Q = pi(P1P2)r4/8etaL, where Q is the volume flow per unit time, r is the radius of the tube of length L, (P1P2) is the pressure difference between the two ends of the tube, and eta is the coefficient of viscosity of the fluid. When one end of the tube is placed at depth h below the surface of the open vertical column of fluid of density rho cross section A, the pressure difference is simply rhogh when the other end of the tube is open to atmosphere. By applying the continuity equation where the volume flow rate at the top of the vertical column is expressed as Av = Adh/dt, where v is the instantaneous speed, it is readily found that the height of the column is given by h = h0exp(–lambdat), where h0 is the column height above the tube at a reference time of t = 0 and

<i>lambda</i>   =   <i>pi</i> <i>rho</i> <i>g</i><i>r</i><sup>4</sup>/8 <i>eta</i> <i>L</i><i>A</i>.


Previous section: BODY OF ARTICLE
Next section: Exponential Decay Experiment
Title Page