Question

Ball 2 is in the water 20 cm above Ball 3. What is the approximate difference in pressure between the 2 balls

Answer 1

The approximate difference in pressure between the two balls is 1961.4 pascals.

Procedure - Pressure difference between two balls at distinct heights and submerged in the same fluid

Mathematical model for difference in pressure

The difference in pressure between the two balls is expressed by a formula derived from the concept of manometric pressure ($\Delta p$), in pascals:

$\Delta p = \rho\cdot g\cdot \Delta h$ (1)

Where:

• $\Delta h$ - Height difference between balls 2 and 3, in meters.
• $\rho$ - Water density, in kilograms per cubic meter.
• $g$ - Gravitational acceleration, in meters per square second.

Calculation of the difference in pressure

If we know that $\rho = 1000\,\frac{kg}{m^{3}}$, $g = 9.807\,\frac{m}{s^{2}}$ and $\Delta h = 0.2\,m\,(20\,cm)$, then the difference in pressure is:

$\Delta p = \left(1000\,\frac{kg}{m^{3}} \right)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.2\,m)$

$\Delta p = 1961.4\,Pa$

The approximate difference in pressure between the two balls is 1961.4 pascals.

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