
A legendary Dutch boy saved Holland by plugging a hole of diameter in a dike with his finger. If the hole was below the surface of the North Sea ( ).
If he pulled his finger out of the hole, during what time interval would the release water fill acre of land to a depth of ? Assume the hole remained of land to a depth of ?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 be the height from top surface at which Dutch boy plugged a hole of given diameter or where is the radius of the hole. And let denote the point where hole is made and is the point at the topmost surface.
Now, we have
Let be the pressure at both points which are at top and at hole.
Then by using Bernoulli theorem we can write as:
Where is the velocity at hole.
Or
Put in above equation we get,
On putting the values of and we get,
Now, Let denotes for the rate of the fluid and it’s calculated as where and be the area of the hole so,
Now, as we know that volume of
So, in order to find time we can simple use where and on putting these values we get,
Or
Hence, of volume will be filled in .
Note: It should be remembered that, the basic units of conversions are as and the velocity of fluid at topmost point is zero because no water flows through this point and remember to notice the height as the difference in distances from ground level to topmost point and the distance from ground level to the point where hole is made.
Complete step-by-step solution:
Let us first draw the diagram. Let

Now, we have
Let
Then by using Bernoulli theorem we can write as:
Where
Or
Put
On putting the values of
Now, Let
Now, as we know that volume of
So, in order to find time we can simple use
Or
Hence,
Note: It should be remembered that, the basic units of conversions are as
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