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A legendary Dutch boy saved Holland by plugging a hole of diameter 1.20cm in a dike with his finger. If the hole was 2.00m below the surface of the North Sea ( density=1030Kgm3 ).
If he pulled his finger out of the hole, during what time interval would the release water fill 1 acre of land to a depth of 1ft ? Assume the hole remained of land to a depth of 1ft ?Assume the hole remained constant in size.

Answer
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Hint : In order to solve this equation, we will use the concept of Bernoulli theorem of fluid mechanics which states that “the sum of the pressure energy, Kinetic energy, and potential energy per unit mass of an incompressible, non-viscous fluid in a streamlined flow always remains a constant”.

Complete step-by-step solution:
Let us first draw the diagram. Let h be the height from top surface at which Dutch boy plugged a hole of given diameter d=1.2cm or r=0.06m where r is the radius of the hole. And let (1) denote the point where hole is made and (2) is the point at the topmost surface.
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Now, we have
ρ=1030Kgm3
y2y1=h=2m
Let P0 be the pressure at both points which are at top and at hole.
Then by using Bernoulli theorem we can write as:
P0+ρgy1+12ρv12=P0+ρgy2+0
Where v1 is the velocity at hole.
12ρv12=ρgy2ρgy1
Or
v1=2g(y2y1)
Put y2y1=h=2m in above equation we get,
v1=2gh
On putting the values of g=9.8msec2 and h=2m we get,
v1=4×9.8
v1=6.26msec1
Now, Let R denotes for the rate of the fluid and it’s calculated as R=A1v1 where v1=6.26msec1 and A1=π(0.06)2m2 be the area of the hole so,
R=6.26×3.14×(0.0036)
R=7.09×104m3sec1
Now, as we know that volume of 1acreft=1.236×103m3
So, in order to find time we can simple use R=Vt where R=7.09×104m3sec1 and V=1.236×103m3 on putting these values we get,
t=1.236×103m37.09×104m3sec1
Or
t=1.74×106sec
Hence, 1acreft=1.236×103m3 of volume will be filled in t=1.74×106sec .

Note: It should be remembered that, the basic units of conversions are as 1cm=0.01m and the velocity of fluid at topmost point is zero because no water flows through this point and remember to notice the height h as the difference in distances from ground level to topmost point and the distance from ground level to the point where hole is made.
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