the pressure at the bottom of a cylindrical container with a cross-sectional area of 57.5 cm2 and holding a fluid of density 640 kg/m3 is 115 kpa. (a) determine the depth of the fluid. m (b) determine the pressure at the bottom of the container if an additional 1.80 10-3 m3 of this fluid is added to the container. (give your answer to at least 3 significant figures.) kpa

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16-12-2022
Physics

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the pressure at the bottom of a cylindrical container with a cross-sectional area of 57.5 cm2 and holding a fluid of density 640 kg/m3 is 115 kpa. (a) determine the depth of the fluid. m (b) determine the pressure at the bottom of the container if an additional 1.80 10-3 m3 of this fluid is added to the container. (give your answer to at least 3 significant figures.) kpa

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wendle1122 wendle1122 · Answer 1 · 2022-12-17T10:29:47-05:00

To determine the depth of the fluid in the cylindrical container, we can use the formula for hydrostatic pressure:

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 fluid column.

Substituting the given values into this formula, we get:

115 kPa = (640 kg/m^3)(9.8 m/s^2)h

Solving for h, we find that the height of the fluid column is:

h = 115 kPa / (640 kg/m^3)(9.8 m/s^2)

= 0.18 m

To determine the pressure at the bottom of the container if an additional 1.80 x 10^-3 m^3 of this fluid is added to the container, we need to use the formula for the volume of a cylinder:

V = πr^2h

Where V is the volume, π is approximately 3.14, r is the radius of the cylinder, and h is the height of the fluid column.

If we assume that the radius of the cylinder is half of the cross-sectional area (in other words, that the cross-sectional area is a circle), we can use the following formula to find the radius:

r = √(A/π)

Where A is the cross-sectional area and π is approximately 3.14.

Substituting the given values into this formula, we find that the radius of the cylinder is:

r = √(57.5 cm^2/3.14)

= 3.58 cm

We can now use this value to find the height of the fluid column after the additional volume has been added:

1.80 x 10^-3 m^3 = (3.14)(3.58 cm)^2h

h = 1.80 x 10^-3 m^3 / (3.14)(3.58 cm)^2

= 0.0005 m

This is a small increase in the height of the fluid column, so we can assume that the pressure at the bottom of the container will not change significantly. The pressure at the bottom of the container will therefore remain approximately 115 kPa to at least 3 significant figures.