Chapter 10, Problem 21Q

To determine

To Explain: Whether the water will come out from the holes of the Styrofoam cup when the cup is dropped freely.

Explanation of Solution

Introduction:

According to the Bernoulli’s principle, the pressure inside the fluid system inversely deals with the volume of the system. The pressure decreases with the increase in the volume of the fluid system and vice-versa. When there is a pressure difference across the body, it causes a push on the body from the region of high pressure to that of low pressure.

The static pressure of the liquid equals the product of the depth of the liquid, the density of the liquid and the gravitational attraction’s strength. When the cup is dropped freely towards the earth then the acceleration of the cup with water cancels out the effect of the gravity effectively. So, in this case the static pressure of the liquid is zero. The dropping rate of the liquid is proportional to the pressure difference, the losses in the hole and the hole’s size.

  $leakrate=\frac{pressure\times hole\text{'}ssize}{lossfactor}$

As the pressure reaches zero and hence, the leak rate also reaches to zero. Therefore, when the cup dropped freely towards the earth in a vacuum then no water is a leak through the holes.

Conclusion:

So, when the Styrofoam cup dropped freely towards the earth in a vacuum then no water is a leak through the holes.