Answer:
Step-by-step explanation:
To solve this problem, we can use the hydrostatic equation:
P = ρgh
where P is the absolute pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.
Given that the tank is in a partial vacuum with an ambient pressure of 1/2 atmosphere, the absolute pressure at the surface of the glycerin will be:
P1 = 1/2 atm + 1 atm = 3/2 atm
Since the tank is filled with glycerin, we can look up its density from a table or use the value of 1260 kg/m³.
The depth of the glycerin in the tank is given as 30 cm = 0.3 m.
The acceleration due to gravity is 9.81 m/s².
Using these values, we can calculate the absolute pressure at the bottom of the tank:
P2 = ρgh + P1
= (1260 kg/m³) x (9.81 m/s²) x (0.3 m) + (3/2 atm x 101325 Pa/atm)
≈ 44753 Pa or 0.44 atm
Therefore, the absolute pressure at the bottom of the tank is approximately 0.44 atm.