Calculate the rate of flow of glycerine of density 1.25×103kgm−3 through the conical section of a pipe, if the radii of its ends are0.1 m and 0.04 m and the pressure drop across its length is 10Nm−2

Question

Calculate the rate of flow of glycerine of density 1.25×103kgm−3 through the conical section of a pipe, if the radii of its ends are0.1 m and 0.04 m and the pressure drop across its length is 10Nm−2

Answer 1

p + (1/2) rho v^2 =constant

and
v2 A2 = v1 A1

v2 (pi * 0.04^2) = v1 (pi * 0.1^2)
so
v2 = (0.01 / 0.0016) v1
= 6.25 v1

p2 +(1/2) rho (6.25 v1)^2 = p1 + (1/2)rho(v1^2)
so
p1 - p2 = (1/2) rho ( 6.25^2 -1) v1^2 = 10