A basketball is pressurized to a gauge pressure of PG 75 kPa when at the surface ofa swimming pool (Patm 101 kPa). The ball is then submerged in the pool of water which has a density p - 1000 kg/m. Assume the ball does not change in mass, Po or volume as it is submerged. Calculate the absolute pressure inside the basketball in kPa when it is at the surface.

P = 176 KPa

Explanation:

Given:-

- The gauge pressure of the basket-ball, PG = 75 KPa

Find:-

Calculate the absolute pressure inside the basketball in kPa when it is at the surface.

Solution:-

- The conversion of gauge pressure to absolute pressure is fairly simple.

- The gauge pressure of any object is pressure of the object relative to the atmospheric pressure (Patm = 1 atm = 101 KPa.

- The conversion relation between gauge and atmospheric pressures is given:

P_abs = Patm + PG

- Use the given gauge pressure of the basketball PG = 75 KPa

P_abs = (101 + 75) KPa

P_abs = 176 KPa

- The absolute pressure of basketball at the surface of the water is P = 176 KPa

Guage pressure inside the basketball when at the surface is 176 kPa.

Explanation:

When at the surface, the ball experiences the force of atmospheric pressure alongside its internal Guage pressure.

Absolute pressure inside the basketball at the surface of the pool is the total of the Guage pressure within the basketball, and the atmospheric pressure.

Pab = Pg + Patm

Pab = 75 kpa + 101 kPa = 176 kPa