Problem #0076 Mechanics Sub-menu Problem #0078 Chapters Chapters

77 (a).

Problem 15.75P (HRW)

A tank is filled with water to a height H. A hole is punched in one of the walls at a depth h below the water surface. We have to show (a) that the distance x from the base of the tank to the point at which the resulting stream strikes the floor is given by . (b) We have to find whether another hole can be punched at another depth to produce a second stream that would have the same range. (c) We have to find the depth at which a hole will give the maximum distance from the base of the tank.

 

 

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Speed with which liquid flows out at depth h is .

Time t taken by the stream for free-fall a height H-h vertically is given by

Horizontal distance x traversed by stream of liquid in time t is

As this function is symmetric in and h, stream coming out of another hole at a depth H-h from the top of the liquid level in the tank will also have the same range x.

We next find h for which will give maximum range x. This will be given by the solution of the equation

That is

Its solution is

Stream from a hole at depth H/2 will have the maximum horizontal range.