(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 23.2 m. Assume the density of the water is 1.00 103 kg/m3 and the air above is at a pressure of 101.3 kPa.
Pa
(b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 33.1 cm?
N
a)
Density of H2O = 1E^3 = 1000kg/m^3
Pair = 101.3 = 101300 Pa
Pwater = (Density of H2O)*Depth*gravity
Ptotal = Pair + Pwater
b)
diameter = 33.1cm
r = 1/2 diameter
Area = pi*r^2
Force = Ptotal * Area
you all suk
(a) Well, to calculate the absolute pressure at the bottom of the lake, we need to consider the pressure due to the water column and the atmospheric pressure above it. So, let's get to the bottom of it!
The pressure due to the water column can be calculated using the hydrostatic pressure formula:
P = ρgh
Where:
P = Pressure
ρ = Density of water
g = Acceleration due to gravity
h = Depth
Plugging in the values:
P = (1.00 * 10^3 kg/m^3) * (9.8 m/s^2) * (23.2 m)
Now, we need to add the atmospheric pressure to this value to get the absolute pressure:
P_absolute = P + atmospheric pressure
Since the atmospheric pressure is given in kilopascals (kPa), let's convert it to pascals (Pa):
atmospheric pressure = 101.3 kPa * 1000 Pa/kPa
Now, we can calculate the absolute pressure:
P_absolute = P + atmospheric pressure
I know it's a bit scientific, but I'm not clowning around when it comes to calculations! Let me do the math for you.
Solution:
P = (1.00 * 10^3 kg/m^3) * (9.8 m/s^2) * (23.2 m)
atmospheric pressure = 101.3 kPa * 1000 Pa/kPa
P_absolute = P + atmospheric pressure
(b) Now, let's calculate the force exerted by the water on the window of the underwater vehicle. We can use the formula:
F = P * A
Where:
F = Force
P = Pressure
A = Area of the window
The area of the circular window can be calculated using the formula:
A = π * (d/2)^2
Plugging in the values:
A = π * (33.1 cm/2)^2
Finally, we can calculate the force:
F = P * A
Don't worry, I won't clown around with the math! Let me calculate it for you.
Solution:
A = π * (33.1 cm/2)^2
F = P * A
(a) To calculate the absolute pressure at the bottom of a fresh-water lake, we can use the formula:
P = P0 + ρgh
where:
P is the absolute pressure at the bottom of the lake,
P0 is the atmospheric pressure at the surface (101.3 kPa),
ρ is the density of the fresh water (1.00 x 10^3 kg/m^3),
g is the acceleration due to gravity (9.8 m/s^2), and
h is the depth of the lake (23.2 m).
First, we need to convert the atmospheric pressure from kilopascals (kPa) to pascals (Pa):
P0 = 101.3 kPa = 101.3 x 10^3 Pa
Now we can plug the values into the formula and solve for P:
P = 101.3 x 10^3 Pa + (1.00 x 10^3 kg/m^3)(9.8 m/s^2)(23.2 m)
Calculating this, we get:
P ≈ 226,016 Pa
So, the absolute pressure at the bottom of the fresh-water lake is approximately 226,016 Pa.
(b) To calculate the force exerted by the water on the window of an underwater vehicle, we can use the formula:
F = P x A
where:
F is the force exerted by the water,
P is the pressure at the bottom of the lake (which we calculated in part (a), approximately 226,016 Pa), and
A is the area of the circular window.
The area of a circular window can be calculated using the formula:
A = πr^2
where:
A is the area,
π is a mathematical constant, approximately equal to 3.14159, and
r is the radius of the window.
Given that the diameter (D) of the window is 33.1 cm, we can calculate the radius (r) as half the diameter:
r = D/2 = 33.1 cm / 2 = 16.55 cm
Now we need to convert the radius from centimeters (cm) to meters (m):
r = 16.55 cm = 16.55 x 10^-2 m
Next, we can calculate the area (A) using the formula:
A = πr^2 = 3.14159 x (16.55 x 10^-2 m)^2
Calculating this, we get:
A ≈ 0.085 m^2
Finally, we can plug the values into the formula for force (F) and solve for F:
F = (226,016 Pa) x (0.085 m^2)
Calculating this, we get:
F ≈ 19,205 N
So, the force exerted by the water on the window of the underwater vehicle at this depth is approximately 19,205 N.
asa
a.) 116kpa
b.) 52 Pa