GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 14 of 65

Marks: +1, -0

A circular duct carrying water gradually contracts from a diameter of

30 {cm}

15 {cm}

. The figure (not drawn to scale) shows the arrangement of differential manometer attached to the duct.

When the water flows, the differential manometer shows a deflection of

8 {cm}

of mercury (Hg). The values of specific gravity of mercury and water are

13.6

and

1.0

, respectively. Consider the acceleration due to gravity,

{g}=9.81 {m} {/} {s}^{2}

. Assuming frictionless flow, the flow rate (in

{m}^{3} {/} {s}

, round off to 3 decimal places) through the duct is___________

Solution:

h=x(\;{G_{n}}/{G_{w}}-1)

h=8(\;{13.6}/{1}-1)

h=100.8 {cm}=1.008 {m}

Flow rate

{Q}=\;{ {A}_{1} {A}_{1}}/{√{A_{1}^{2}- {A}_{2}^{2}} √{2 g h}}

{A} 1=4 {A}_{2}, {g} 9.81 {m} {/} {sec}^{2}

A_{2}=\;{π}/{4} × 0.15^{x}

\;\; =0.01767 {m}^{2}

Q=\;{4 A_{1}^{2}}/{√{16 A_{2}^{2}-A_{2}^{2}}} √{2 × 9.81 × 1.008}

\;\; =\;{4 A_{2}}/{√{15}} √{19.777}

Q=\;{4 ×(0.01767)}/{√{15}} √{19.777}

Q=0.081 {m}^{2} {/} sec

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