SSC JE Mechanical Engineering 27 Sep 2019 Shift 2 Paper

Question : 169 of 200

Marks: +1, -0

The difference of the pressure head (h) measured by a differential U tube manometer used for the measurement of difference in pressure of an oil flowing through a pipe is given by which of the following equation?
Where,

{S}_{{m}}=

Specific gravity of the monometric liquid (mercury),

{S}_{0}=

Specific gravity of oil,

{x}

=

deflection of the mercury level.

${h}={x}[({S}_{{m}} \/ {S}_{0}-1)]$
${h}={x}[1-({S}_{{m}} \/ {S}_{{o}})]$
$h=x(S_{m}-S_{o})$
${h}={x}({S}_{0}-{S}_{{m}})$

Validate

Solution:

Equating pressure on both the sides we get;

P_{a}+\ρ_{\text "oil "} g x=P_{b}+\ρ_{m} g x

P_{a}-P_{b}=\ρ_{m} g x-\ρ_{\text "oil "} g x

P_{a}-P_{b}=g x(\ρ_{m}-\ρ_{\text "oil "})

P a-P b=g x \ρ_{\text "oil "}({\ρ_{m}}/{\ρ_{\text "oil "}}-1)

{P_{a}-P_{B}}/{g \ρ_{\text "oil "}}=x({{\ρ_{m}}/{\ρ_{\text "gtd "}}}/{{\ρ_{\text "oil "}}/{\ρ_{\text "gtd "}}}-1)

h=x({S_{m}}/{S_{\text "oil "}}-1)

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