Final answer:
The tank level for sulfuric acid with an SG of 1.8 and a 9.5 mA reading from the pressure transmitter is approximately 0.304 feet.
Step-by-step explanation:
To calculate the tank level using the pressure transmitter reading, we use the relationship between pressure, specific gravity (SG), and height of the liquid column. The transmitter reading of 9.5 mA corresponds to a certain pressure, but we need to understand the relationship between the current and pressure range of the transmitter. Usually, a 4-20 mA signal corresponds to the full range of the sensor. For a 0-60 psig range, 4 mA would correspond to 0 psig and 20 mA to 60 psig. We can map the current to the pressure using the following formula:
Pressure (psig) = ((Current mA) - 4 mA) / (20 mA - 4 mA) × (Max Range psig)
Substituting the measured current value:
Pressure (psig) = ((9.5 mA) - 4 mA) / (20 mA - 4 mA) × 60 psig = 22.5 psig
The pressure exerted by the liquid column is given by:
P = ρgh
Where:
- P is the pressure exerted by the liquid column (in psi).
- ρ is the density of the liquid (in slug/ft³).
- g is the acceleration due to gravity (32.174 ft/s²).
- h is the height of the liquid column (in ft).
Solving for h (height), we get:
h = P / (ρg)
The SG is given as 1.8, which means the density of the acid is 1.8 times the density of water (62.4 lb/ft³).
Thus,:
ρ = SG × density of water
Plugging in this information to find the height:
h = 22.5 psi / (1.8 × 62.4 lb/ft³ × 32.174 ft/s²)
h = 22.5 psi / (1.8 × 62.4 lb/ft³ × 32.174 ft/s²)
h ≈ 0.304 ft (approximately)
The tank level for sulfuric acid with an SG of 1.8 and a pressure reading equivalent to 9.5 mA current from the transmitter is approximately 0.304 feet.