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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

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Here, `rho=1.25 xx 10^(3) kg//m^(3) , r_(1) = 0.1 m, r_(2) = 0.04 m , P_(1)-P_(2) = 10 N//m^(2)`
Now `a_(1) = pi r_(1)^(2) and a_(2) = pi r_(2)^(2)`
Volume of the glycerine flowing per second through conical tube is
`V= a_(1)a_(2) sqrt((2(P_(1)-P_(2)))/(rho(a_(1)^(2)-a_(2)^(2)))) = pir_(1)^(2) xx pir_(2)^(2) sqrt((2xx10)/((1.25xx10^(3))xx[(pi r_(1)^(2))^(2)-(pir_(2)^(2))^(2)]))`
`= 22/7 xx (0.1)^(2) xx 22/7 xx (0.04)^(2) sqrt((2xx10)/((1.25 xx 10^(3)) xx [{22/7 xx(0.1)^(2)}^(2)-{22/7 xx (0.04)^(2)}^(2)]))`
`= 6.44 xx 10^(-4) m^(3)//s`.
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