GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 59 of 65

Marks: +1, -0

In a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are

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

and

0.25 {m}{/} {s}

, respectively. If the full scale structure ( 30 times bigger) is subjected to a discharge of

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

, then the time scale (model to full scale) value (up to two decimal places) is______________

Solution:

Froude Law

\;\; ( {Fr})_{ {m}}=( {Fr})_{ {p}}

(\;{V}/{√{L g}})_{m}=(\;{V}/{√{L g}})_{p} \;\; (g_{m}=g_{p})

V_{r}=√{L_{r}}

\;\; \;{L_{r}}/{T_{r}}=√{L_{r}}

T_{r}=√{L_{r}}

T_{r}=√{\;{1}/{30}}=0.1826

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