A circular membrane lies 24cm below the open surface of a pool of mercury of relative density 13.6.If the barometric height of 76 cm of mercury, the pressure on the membrane is
Not 100% sure but maybe just convert the cm of mercury to mmHg because mmHg is a unit of pressure and you got your answer
To find the pressure on the membrane, we need to consider two factors: the pressure due to the column of mercury above the membrane and the pressure due to the pool of mercury below the membrane.
Let's break this down step-by-step:
1. Calculate the pressure due to the column of mercury above the membrane:
The pressure due to a column of fluid is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the column of fluid.
In this case, the density of mercury is given as 13.6 times that of water, which means its relative density is 13.6. Since the barometric height is given as 76 cm, the height h for the column of mercury above the membrane is 76 cm. Substituting these values into the formula, we get:
P1 = (13.6 * 1000 kg/m³) * (9.8 m/s²) * (0.76 m)
2. Calculate the pressure due to the pool of mercury below the membrane:
The pressure due to the pool of mercury below the membrane only depends on the depth, not on the density of the fluid. So, we can use the formula P = ρgh again, but this time the height h is the distance from the membrane to the surface of the pool. Given that the circular membrane lies 24 cm below the open surface of the pool, the height is 24 cm. Substituting these values into the formula, we get:
P2 = (1000 kg/m³) * (9.8 m/s²) * (0.24 m)
3. Calculate the total pressure on the membrane:
The total pressure on the membrane is the sum of the pressures calculated in steps 1 and 2:
Total Pressure = P1 + P2
Now, let's calculate the values:
P1 = (13.6 * 1000 kg/m³) * (9.8 m/s²) * (0.76 m)
P1 ≈ 128744.32 Pa (Pascals)
P2 = (1000 kg/m³) * (9.8 m/s²) * (0.24 m)
P2 ≈ 2352.00 Pa
Total Pressure = P1 + P2
Total Pressure ≈ 131096.32 Pa
Therefore, the pressure on the membrane is approximately 131096.32 Pa.