Question

The water level in an open vessel is to be monitored by a differential pressure cell responding to the difference in pressure between that at the base of the vessel and the atmosphere. Determine the range of differential pressures the cell will have to respond to if the water level can vary between zero height above the cell measurement point and 2 m above it.

Answer 1

The differential pressure range a cell has to respond to when monitoring water levels from 0 to 2 meters is from 0 Pa to roughly 19620 Pa, calculated using the formula for hydrostatic pressure (p = ρgh) and considering the density of water and acceleration due to gravity.

Step-by-step explanation:

The range of differential pressures the cell would have to respond to can be determined by calculating the hydrostatic pressure at different water levels. Hydrostatic pressure is the pressure exerted by a fluid due to gravity. In the case of water at a level from zero to 2 meters above the measurement point, the pressure can be calculated using the formula p = ρgh, where:

• ρ is the density of water (approximately 1000 kg/m³ at room temperature)
• g is the acceleration due to gravity (9.81 m/s²)
• h is the height of the water column above the measurement point

The atmospheric pressure is not exerting additional force on the water in an open vessel, as it is equaled out by the same atmospheric pressure acting on the differential pressure cell's reference side (measure of atmospheric pressure). Therefore, for a water height of 0 meters, the hydrostatic pressure is 0 Pa, and for a water height of 2 meters, it is:

p = 1000 kg/m³ × 9.81 m/s² × 2 m = 19620 Pa (or roughly 0.194 atm)

The differential pressure range for the sensor would need to be from 0 Pa (when the water level is at the cell measurement point) to approximately 19620 Pa (when the water level is 2 m above the measurement point).