A liquid of coefficient of viscosity `eta=1` poise is flowing in a pipe of radius 3 cm such that the rate of volume flow is `1000 l//min`.Determine the Reynolds numbers. (A) 3536 (B) 3500 (C) 3400 (D) 3600

A liquid of density 10 ^(3) kg/m^(3) and coefficient of viscosity 8 xx10^(-2) decapoise is flowing in a tube of radius 2 cm with speed 2 m/s. The. Reynold’s number is

Reynolds number for a liquid of density rho , viscosity eta and flowing through a pipe of diameter D, is given by

Water flows at a speed 5 cm s^(-1) through a pipe of radius 2 cm. The visosity of water is 0.001 PI. The Reynolds number and the nature of flow are respectively

Volume rate flow of a liquid of density rho and coefficient of viscosity eta through a cylindrical tube of diameter D is Q. Reynold's number of the flow is

When a viscous liquid flows , adjacent layers oppose their relative motion by applying a viscous force given by F = - eta A (dv)/(dz) where , eta = coefficient of viscosity , A = surface area of adjacent layers in contact , (dv)/(dz) = velocity gradient Now , a viscous liquid having coefficient of viscosity eta is flowing through a fixed tube of length l and radius R under a pressure difference P between the two ends of the tube . Now consider a cylindrical vloume of liquid of radius r . Due to steady flow , net force on the liquid in cylindrical volume should be zero . - eta 2pirl (dv)/(dr) = Ppir^(2) - int _(v)^(0),dv = P/(2 eta l) int_(tau)^(R) rdr ( :' layer in contact with the tube is stationary ) v = v_(0) (1- (r^(2))/(R^(2))) , where v_(0) = (PR^(2))/(4nl) :. " " Q = (piPR^(4))/(8sta l) This is called Poisecuille's equation . The velocity of flow of liquid at r = R/2 is

When a viscous liquid flows , adjacent layers oppose their relative motion by applying a viscous force given by F = - eta A (dv)/(dz) where , ete = coefficient of viscosity , A = surface area of adjacent layers in contact , (dv)/(dz) = velocity gradient Now , a viscous liquid having coefficient of viscosity eta is flowing through a fixed tube of length l and radius R under a pressure difference P between the two ends of the tube . Now consider a cylindrical vloume of liquid of radius r . Due to steady flow , net force on the liquid in cylindrical vloume should be zero . - eta 2pirl (dv)/(dr) = Ppir^(2) - int _(v)^(0),dv = P/(2 eta l) int_(tau)^(R) rdr ( :' layer in contact with the tube is stationary ) v = v_(0) (1- (r^(2))/(R^(2))) , where v_(0) = (PR^(2))/(4nl) :. " " Q = (piPR^(4))/(8sta l) This is called Poisecuille's equation . The volume of the liquid flowing per sec across the cross - section of the tube is .

When a viscous liquid flows , adjacent layers oppose their relative motion by applying a viscous force given by F = - eta A (dv)/(dz) where , ete = coefficient of viscosity , A = surface area of adjacent layers in contact , (dv)/(dz) = velocity gradient Now , a viscous liquid having coefficient of viscosity eta is flowing through a fixed tube of length l and radius R under a pressure difference P between the two ends of the tube . Now consider a cylindrical vloume of liquid of radius r . Due to steady flow , net force on the liquid in cylindrical volume should be zero . - eta 2pirl (dv)/(dr) = Ppir^(2) - int _(v)^(0),dv = P/(2 eta l) int_(tau)^(R) rdr ( :' layer in contact with the tube is stationary ) v = v_(0) (1- (r^(2))/(R^(2))) , where v_(0) = (PR^(2))/(4nl) :. " " Q = (piPR^(4))/(8etaL) This is called Poisecuille's equation . The viscous force on the cylindrical volume of the liquid varies as

A cone whose height always equal to its diameter is increasing in volume at the ran 40 (cm^3)/sec .At what rate is the radius increasing when its circular base area is 1m^2? (A) 1 (B) 0.001 (C) 2 (D) 0.002

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Blood vessel is 0.10 m in length and has a radius of 1.5xx10^(-3) m blood flows at rate of 10^(-7)m^(3)//s through this vessel. The pressure difference that must be maintained in this flow between the two ends of the vessel is 20 Pa what is the viscosity sufficient of blood?

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Calculate the highest average speed that blood (rho~~1000kg//m^(3) ) could have and still remain in laminar flow when it flows through the arorta (R=8xx10^(-3)m ) Take the coeffiicient of viscosity of blood to be 4xx10^(-3)Pa-s