1. The water pressure in a kitchen faucet is 3.43 x 10^5 N/m^2. How high above the faucet is the surface of the water in the storage tank?
2. A swimming pool 8.0 m x 15.0 m has a uniform depth of 2.0 m. Determine the total force and the absolute pressure on the bottom of the pool.
3. A force of 30N from a nail is applied to a square tile 15 cm on a side. What is the stress on the tile?
35
2.
Force = 2352000 N
pressure = 19600 Pa
1. To determine the height above the faucet of the water surface in the storage tank, we can use the equation for pressure at a given height in a fluid.
Pressure = density x gravity x height
Let's assume the density of water is 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2.
Given:
Water pressure in the faucet = 3.43 x 10^5 N/m^2
Using the equation for pressure, we can rearrange it to solve for height:
Height = Pressure / (density x gravity)
Substituting the given values:
Height = (3.43 x 10^5 N/m^2) / (1000 kg/m^3 x 9.8 m/s^2)
Height ≈ 35.00 meters
Therefore, the surface of the water in the storage tank is approximately 35 meters above the faucet.
2. To find the total force and absolute pressure on the bottom of the swimming pool, we can use the equation for pressure in a fluid.
Pressure = density x gravity x depth
Let's assume the density of water is 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2.
Given:
Pool dimensions: length = 8.0 m, width = 15.0 m, depth = 2.0 m
Using the equation for pressure, we can calculate the total force on the bottom of the pool:
Total Force = Pressure x Area
Area = length x width
Total Force = (density x gravity x depth) x (length x width)
Substituting the given values:
Total Force = (1000 kg/m^3 x 9.8 m/s^2 x 2.0 m) x (8.0 m x 15.0 m)
Total Force ≈ 2.35 x 10^6 N
The total force on the bottom of the pool is approximately 2.35 x 10^6 Newtons.
To calculate the absolute pressure on the bottom of the pool, we can use the equation for pressure:
Absolute Pressure = Pressure at a specific point + Pressure due to fluid column
At the bottom of the pool, the pressure due to the fluid column is equal to the total force divided by the area.
Area = length x width
Absolute Pressure = (Total Force / Area) + Pressure at a specific point
Substituting the given values:
Absolute Pressure = (2.35 x 10^6 N) / (8.0 m x 15.0 m) + Pressure at a specific point
The specific point at which the pressure is measured is not provided in the question. So, the value of the absolute pressure will depend on the specific point chosen.
3. To determine the stress on the square tile, we need to use the equation for stress.
Stress = Force / Area
Given:
Force applied from the nail = 30 N
Area of the square tile = side x side
Area = (15 cm) x (15 cm)
Convert cm to m:
1 cm = 0.01 m
Area = (15 cm x 0.01 m/cm) x (15 cm x 0.01 m/cm)
Area = 0.225 m^2
Now we can calculate the stress:
Stress = (30 N) / (0.225 m^2)
Stress ≈ 133.33 N/m^2 or 133.33 Pascal (Pa)
Therefore, the stress on the square tile is approximately 133.33 N/m^2 or 133.33 Pa.
To answer these questions, you'll need to use the concepts of pressure and stress. Here's how you can calculate the answers:
1. To determine the height of the water in the storage tank, you can use the concept of hydrostatic pressure. The formula for hydrostatic pressure is P = ρgh, where P is the pressure, ρ is the density of the fluid (water in this case), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the fluid column.
In this case, you are given the pressure, P, as 3.43 x 10^5 N/m^2. Since the density of water is approximately 1000 kg/m^3, you can substitute these values into the hydrostatic pressure formula and solve for h.
P = ρgh
3.43 x 10^5 N/m^2 = (1000 kg/m^3) x (9.8 m/s^2) x h
Solving for h, you find:
h = (3.43 x 10^5 N/m^2) / ((1000 kg/m^3) x (9.8 m/s^2))
2. To calculate the total force and absolute pressure on the bottom of the pool, you can use the formula for pressure P = ρgh, where P is the pressure, ρ is the density of the fluid (water in this case), g is the acceleration due to gravity, and h is the depth of the fluid.
In this case, you are given the depth, which is 2.0 m, and the acceleration due to gravity is approximately 9.8 m/s^2. The density of water is still approximately 1000 kg/m^3.
Using the formula, you can calculate the pressure:
P = (1000 kg/m^3) x (9.8 m/s^2) x (2.0 m)
To find the total force, you can multiply the pressure by the surface area of the pool, which is given as 8.0 m x 15.0 m.
Total force = (Pressure) x (Surface area)
Total force = P x (8.0 m x 15.0 m)
3. To find the stress on the square tile, you can use the formula for stress, which is defined as the force divided by the area. In this case, the force is given as 30 N and the side length of the tile is 15 cm.
First, convert the side length to meters, which will be 0.15 m. Then, calculate the stress using the formula:
Stress = Force / Area
Stress = 30 N / (0.15 m x 0.15 m)