Problem 154P

An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Fig. P10-46. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by P = CDn, where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.

Solution

Step 1 of 10

In a partially water filled tank, an elastic balloon is attached to the base of the tank which is immersed inside the water as shown in the figure below. The initial diameter is given to be . Here we need to calculate the change in cable tension force of the when the pressure in the tank is increased from to , where the relation between the pressure and diameter is given to be .