Visualize an image that represents a hydraulic system with two pistons. Piston A with a wider cross-section area, approximately 1200 sq.cm., and Piston B with a slightly smaller area, around 950 sq.cm. Place Piston B higher than Piston A by 1.75m in the image. The system in between is filled with a translucent fluid representing oil simulating the specific gravity of 0.80. The scene should be educational and visually pleasing, but the image should not contain any text.

Piston A has a cross section of 1200 sq.cm. While that of piston B is 950 sq.cm. with the latter higher than piston A by 1.75m. If the intervening passages are filled with oil whose specific gravity is 0.80, what is the difference in pressure between A and B

The area does not determine the pressure but only the force when the pressure is known.

All that matters here is the difference in altitude.
B is high
A is low
density * g * 1.75 meters
.8 * 1000 kg/meter^2 * 9.81 * 1.75

= 13,734 Newtons/m^2 or Pascals
one atmosphere is about 100,000 Pascals
so we are talking about 0.13 atmospheres

Well, let's calculate the pressure difference between piston A and piston B. But before we do that, let me just say that these pistons probably don't appreciate being compared like this. They have feelings too, you know! Anyway, let's get back to business.

First, we need to calculate the height difference between piston A and B: 1.75m. Now, since the passages are filled with oil, we need to consider the difference in specific gravity.

Since the specific gravity of oil is 0.80, we can infer that it is less dense than water. So, we need to multiply the height difference by the specific gravity to get the adjusted height difference.

Adjusted height difference = height difference x specific gravity
= 1.75m x 0.80
= 1.4m

Now that we have the adjusted height difference, we can calculate the pressure difference using the formula:

Pressure difference = (density of oil) x (acceleration due to gravity) x (adjusted height difference)

Since specific gravity is defined as the ratio of the density of oil to the density of water, we can rewrite the formula as:

Pressure difference = (specific gravity x density of water) x (acceleration due to gravity) x (adjusted height difference)

Now, we just need to plug in the known values:

Pressure difference = (0.80 x 1000 kg/m³) x (9.8 m/s²) x (1.4m)
= 11,144 Pa

So, the pressure difference between piston A and B is approximately 11,144 Pascal. I hope that answers your question and brings a little humor to the topic!

To find the difference in pressure between piston A and piston B, we need to calculate the pressure at each piston.

Step 1: Calculate the height difference between the two pistons.
Since the height difference between piston A and B is given as 1.75m, we have Δh = 1.75m.

Step 2: Calculate the weight of the oil column above each piston.
The weight of the oil column can be calculated using the formula:
Weight = mass × gravity

The mass of the oil column can be calculated as follows:
mass = density × volume

Considering specific gravity (SG) as the ratio of the density of the oil to the density of water, which is 0.80 in this case, we have:
density_of_oil = SG × density_of_water

Since the density of water is approximately 1000 kg/m^3, we have:
density_of_oil = 0.80 × 1000 kg/m^3 = 800 kg/m^3

Now we can calculate the weight of the oil column above each piston.

Step 2a: Calculate the weight of the oil column above piston A.
volume_of_oil_A = cross_section_A × height_A

cross_section_A = 1200 sq.cm = 0.12 sq.m (since 1 sq.m = 10,000 sq.cm)
height_A = 0m (no oil above piston A)

weight_A = density_of_oil × volume_of_oil_A × gravity

Substituting the given values, we find:
weight_A = 800 kg/m^3 × 0.12 sq.m × 0m × 9.8 m/s^2 = 0 N

Step 2b: Calculate the weight of the oil column above piston B.
volume_of_oil_B = cross_section_B × height_B

cross_section_B = 950 sq.cm = 0.095 sq.m (since 1 sq.m = 10,000 sq.cm)
height_B = 1.75 m

weight_B = density_of_oil × volume_of_oil_B × gravity

Substituting the given values, we find:
weight_B = 800 kg/m^3 × 0.095 sq.m × 1.75m × 9.8 m/s^2

Step 3: Calculate the pressure at each piston.
Pressure = weight / area

pressure_A = weight_A / cross_section_A = 0 N / 0.12 sq.m = 0 Pa

pressure_B = weight_B / cross_section_B

Step 3a: Convert weight_B from Newtons to Pascals (Pa)
1 N = 1 Pa

Substituting the given values, we find:
pressure_B = (800 kg/m^3 × 0.095 sq.m × 1.75m × 9.8 m/s^2) / 0.095 sq.m

Step 4: Calculate the difference in pressure between A and B.
difference_in_pressure = pressure_B - pressure_A

Substituting the calculated values, we find:
difference_in_pressure = (800 kg/m^3 × 0.095 sq.m × 1.75m × 9.8 m/s^2) / 0.095 sq.m - 0 Pa

Simplifying further, we find:
difference_in_pressure ≈ 13,304 Pa

Therefore, the difference in pressure between piston A and piston B is approximately 13,304 Pa.

To find the difference in pressure between pistons A and B, we need to consider the hydrostatic pressure equation. The hydrostatic pressure 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 fluid column.

Given information:
Cross-section area of piston A (Aa) = 1200 sq.cm
Cross-section area of piston B (Ab) = 950 sq.cm
Difference in height (h) = 1.75 m
Specific gravity of oil (σ) = 0.80

First, we need to calculate the fluid density (ρ) using the specific gravity (σ) and the density of water (ρw), which is 1000 kg/m³:

ρ = σ * ρw
= 0.8 * 1000
= 800 kg/m³

To find the pressure difference between A and B, we need to calculate the pressure exerted by the oil on each piston individually.

For piston A:

The height (h1) for piston A is 0 since it is at the same level as the oil, so the pressure exerted by the oil on A (Pa) is:

Pa = ρ * g * h1
= 800 * 9.8 * 0
= 0 Pa

For piston B:

The height (h2) for piston B is 1.75 m, so the pressure exerted by the oil on B (Pb) is:

Pb = ρ * g * h2
= 800 * 9.8 * 1.75
≈ 13,720 Pa

Therefore, the difference in pressure between piston A and B is:

Difference in pressure = Pb - Pa
= 13,720 - 0
= 13,720 Pa

So, the difference in pressure between pistons A and B is approximately 13,720 Pa.