My professor tells me I'm not using the right formula for this problem. can someone please help me. The formula is not delt p = density x gravity x height
The mercury manometer on the right and the pressure transducer on the left are both connected to a piston-driven pressure source filled with hydraulic oil (density = 880 kg/m^3). The bulbs connected to the transducer and the right side of the manometer are both evacuated (denisty = 0). Calculate pressures from the manometer reading.
hL (mm Oil) = 450
Manometer reading = 150
Transducer Output = 5.6 (mA)
To calculate the pressures from the manometer reading, you need to use the correct formula. The formula you provided (delt p = density x gravity x height) is incorrect for this problem.
In this case, you need to use the hydrostatic pressure formula, which is:
P = P₀ + ρgh,
where:
P is the pressure at a specific point,
P₀ is the reference pressure (usually atmospheric pressure),
ρ is the density of the fluid,
g is the acceleration due to gravity,
h is the height or depth of the fluid column.
Let's apply this formula to the given problem:
1. Convert the manometer reading from mm to meters:
hL = 450 mm = 0.45 m.
2. Calculate the pressure due to the oil column using the formula:
P = P₀ + ρgh.
Since the bulb, which is connected to the right side of the manometer, is evacuated (density = 0), the pressure due to the oil column is only present on the left side of the manometer.
P₁ = P₀ + ρgh,
P₁ = P₀ + (880 kg/m³) x (9.8 m/s²) x 0.45 m.
3. Calculate the pressure on the left side of the manometer using the formula:
P = P₀ + ρgh.
Since the bulb connected to the transducer is also evacuated (density = 0), the pressure at the transducer output is only due to the height of the oil column in the left side of the manometer.
P₂ = P₀ + ρgh,
P₂ = P₀ + (880 kg/m³) x (9.8 m/s²) x 0.45 m.
4. Convert the transducer output from mA to A (amperes):
Transducer Output = 5.6 mA = 5.6 x 10⁻³ A.
Now, you can use the given formula and these calculated pressures to find the answers.