Home
Class 11
PHYSICS
Calculate the rate of flow of glycerine ...

Calculate the rate of flow of glycerine of density `1.25xx10^(3) kg m^(-3)` through the conical section of a pipe, if the radii of its ends are`0.1` m and `0.04` m and the pressure drop across its length is `10 Nm^(-2)`.

Text Solution

Verified by Experts

The correct Answer is:
6.53
Using Bernoulli.s theorem for horizontal flow, `p_1+1/2 rhov_1^2=p_2+1/2rhov_2^2`
or `v_2^2-v_1^2=(2(p_1-p_2))/(rho)`
`=(2xx10Nm^(-2))/(1.25 xx10^3 "kgm"^(-3))=16 xx10^(-3)`
According to equation of continuity, `a_1v_1 = a_2 v_2`
`:. v_1/v_2=(a_2)/(a_1)=(pir_2^2)/(pir_1^2)=r_(2)^2/r_(1)^2=((0.04)^2)/((0.1)^2)=16xx10^(-2)`
`v_1 = 16xx10^(-2) v_2`
Hence `v_2^(2) -(16 xx10^(-2)v_2)^(2)=16 xx10^3`
or `v_2^2[1-(256)/10000]=16xx10^(-3)`
or `v_2^2xx(9744)/(10000) = 16 xx10^(-3)`
or `v_2^(2) = (160)/9744 ` or `v_2 = 0.13 "ms"^(-1)`
Rate flow of glycerine `= a_(2) v_(2) = 3.14 xx (0.04)^2 xx 0.13 = 6.53xx10^(-4) m^(3)s^(-1)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Calculate the rate of flow of glycerine of density 1.25 xx 10^(3) kg//m^(3) through the conical section of a pipe if the radii of its ends are 0.1m and 0.04 m and the pressure drop across its lengths is 10N//m^(2) .

Calculate the rate of flow of glycerine of density 1.20 xx 10^(3) kg//m^(3) through the conical section of a pipe. If the radii of its ends are 0.1 m and 0.02 m and the pressure drop across the length is 10 N/m^(2) .

Calculate the rate of flow of glycerine of density. 1.25xx10^(3) kg//m^(3) through the conical section of a pipe. If the radii of its ends are 1.0m and 0.04m and the pressure drop across its length is 10N//m^(2) .

The radii of curvatures of a convex lens are 0.04 m and 0.04m. Its refractive index is 1.5. Its focal length is

Calculate the moment of inertia of a cylinder of length 1.5 m , radius 0.05m and density 8 xx 10^(3) kg//m^(3) about the axis of the cylinder.

In the figure shown below, a fluid of density 2 xx 10^(3) kg m^(-3) is flowing in a horizontal pipe. The speed of water at point A is 4 cm s^(-1) , what is its speed at point B?

A thick rope of rubber of density 1.5 xx 10^(3) kg m^(-3) and Young's modulus 5 xx 10^(6) Nm^(-2) , 8 m in length, when hung from ceiling of a room, the increases in length due to its own weight is

To what height does a liquid of density 0.4 xx 10^(3) kg m^(-3) and surface tension 0.05 Nm^(-1) rise in a capillary tube of radius 0.2 mm when dipped in ? [Given cos theta = 0.4 g = 10 m s^(-2) ]

The workdone by pressure in forcing 1m^3 of water through a pipe if the pressure difference across the pipe is 10^4 Pa, is