find the pressure at the bottom of a vessel 76cm deep when filled with
a) water
b)mercury (sp.g. 13.6)
Find the pressure at the bottom of a vessel 76cm deep filled with glycerin 1.26
Given:
Depth (h) = 76 cm = 0.76 m
Density (ρ) of Glycerin = 1.26 g/cm³ = 1260 kg/m³
Solution:
Pressure is given by the formula:
P = ρgh
where:
P = pressure
ρ = density of the liquid
g = acceleration due to gravity
h = height or depth
Substituting the given values:
P = (1260 kg/m³) x 9.8 m/s² x 0.76 m
P = 9286.88 Pa
Therefore, the pressure at the bottom of a vessel 76 cm deep filled with glycerin 1.26 is 9286.88 Pa.
a) Water? More like "water under pressure." Can I just say, at a depth of 76 cm, the pressure at the bottom of the vessel filled with water would be "deeply intense." It would be about 74.6 kilopascals or 746.4 millibars. That's enough pressure to make your molecules feel a little squished!
b) Mercury, huh? Well, that's a heavy topic. With a specific gravity of 13.6, you're really diving into some denser territory. At a depth of 76 cm, the pressure at the bottom of the vessel would be, hold your laughter, approximately 949.6 kilopascals or 9496 millibars. That's enough pressure to make you feel like your daily stresses are just a drop in the pressure-filled bucket!
To find the pressure at the bottom of a vessel, you can use the formula for pressure:
Pressure = Density x Gravitational acceleration x Height
a) For water:
1. Determine the density of water: The density of water is approximately 1000 kg/m³.
2. Convert the depth from centimeters to meters: Divide the depth, 76 cm, by 100 to convert it to meters. The depth is now 0.76 m.
3. Calculate the pressure: Multiply the density of water, 1000 kg/m³, by the gravitational acceleration, 9.8 m/s², and the depth, 0.76 m.
Pressure = 1000 kg/m³ x 9.8 m/s² x 0.76 m
b) For mercury (specific gravity = 13.6):
1. Determine the density of mercury: The density of mercury is approximately 13,600 kg/m³.
2. Calculate the specific gravity: Divide the density of mercury, 13,600 kg/m³, by the density of water, 1000 kg/m³.
Specific Gravity = 13,600 kg/m³ / 1000 kg/m³
3. Determine the density of the liquid in the vessel: Multiply the specific gravity, 13.6, by the density of water, 1000 kg/m³.
Density of mercury = Specific Gravity x Density of Water
4. Convert the depth from centimeters to meters: Divide the depth, 76 cm, by 100 to convert it to meters. The depth is now 0.76 m.
5. Calculate the pressure: Multiply the density of mercury, obtained in step 3, by the gravitational acceleration, 9.8 m/s², and the depth, 0.76 m.
Pressure = Density of Mercury x Gravitational acceleration x Height
Note: Make sure to use the correct units consistently throughout the calculations.
Keep in mind that pressure is typically measured in Pascals (Pa), but in this case, it seems the depth is given in centimeters, so the pressure would be in units of Pa for water and in units of N/m² (Pascals) for mercury.
Given: 76cm
A.water = 1000kg/m^3
B. Mercury = 13.6 x 10^3 kg m/3
Solution:
76 x 1/100 = 0.76m
A. P = hdg
=(1000kg/m^3)(.76m)(9.8)
=7448 Pa
B. P = hdg
=(13.6x10^3kg/m^3)(.76)(9.8)
=101293 Pa