MECHANICAL PROPERTIES OF FLUID AND LIQUID - Lecture Notes

BBrilliant STUDY CENTRE LT23M - PHYSICS (ONLINE) h  2T cos  rg Put r  R cos  h  2T Rg hR  2T  cons tan t g 2T cos  * If length of the tube is less than rg then liquid will rise to the top of the tube but will not flow out like fountain. In this case free surface of the liquid at the top of the tube becomes fleet R   hR  2T  cons tan t g VISCOSITY It is the internal friction in a liquid, it opposes the relative motion between adjacent layers of liquid   Coefficient of viscosity A  Area of the layers in contact dv  Velocity of gradient dx 51

BBrilliant STUDY CENTRE LT23M - PHYSICS (ONLINE) * Flow of liquid through a cylindrical pipe under the action of viscous force The velocity is maximum along the axis and almost zero at the pipe walls. If P1 and P2 are the pressure at the two ends of a pipe of length L, the flow speed at a radial distance r from the axis of the pipe is given by  V  P1  P2 R2  r2 4L Vmax   P1  P2  R2 4L * Q  dv  volume flow rate dt * Fluid current  Pr essure difference Fluid resis tan ce Q  dv  P1  P2  * dt  8L   R 4  * STOKES LAW Viscous force acting on a small spherical body of radius r falling through a viscous medium is given by F  6rVT VT  Terminal velocity 52

BBrilliant STUDY CENTRE LT23M - PHYSICS (ONLINE) * Body falls with constant speed called terminal speed when its weight is balanced by viscous force and buoyant force. Let  be the density of the material of the spherical drop and  be the density of the medium mg  Fv  Fb mg  6rvT  Fb 4 r3g  6rvT  4 r3g 3 3 4 r3   g  6rvT 3 Ter min al velocity  VT   2r2    g 9 53