A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 10.4 m below the water level. Assume the tank is large so the velocity of the water at the top of the tank is zero. The rate of flow from the leak is 2.53×10^−3 m3/min. Determine the diameter of the hole.

Therefore the diameter of the hole is m.

Step-by-step explanation:

Bernoulli's equation,

P₁ = P₂= atmospheric presser

= density

            [since P₁ = P₂]

                               []

Here  

Here g= 9.8 m/s² , h = 10.4 m

The velocity of water that leaves from the hole = m/s

                                                                                  =14.28 m/s.

Given, the rate of flow from the leak is

Let the diameter of the hole be d.

Then the cross section area of the hole is

We know that,

The rate of flow = Cross section area × speed

Therefore the diameter of the hole is m.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: