GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 57 of 65

Marks: +1, -0

A tank open at the top with a water level of

1 {m}

, as shown in the figure, has a hole at a height of

0.5 {m}

. A free jet leaves horizontally from the smooth hole. The distance

{X}

(in

{m}

) where the jet strikes the floor is

Solution:

Let free jet velocity is x displacement

t=\;{x}/{v}

Velocity of jet coming from the orifice in

X

direction,

v=√{2 g h}

t=\;{x}/{√{2 g h}}

....(i)

To calculate time '

{t}^{'}

, using equation of motion for y direction By second law of motion equation
By second law of motion equation

s=u t+\;{1}/{2} g t^{2}

For free fall

u=0, s=0.5 m

t=√{\;{2 s}/{g}}

t=√{\;{2 × 0.5}/{g}}=\;{1}/{√{g}}

....(ii)
is the time of free fall of object
By equation (i) and (ii)

{x}=1 {m}

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