can someone help me on this? thanks
a viewing window 30cm in diameter is installed 3m below the surface of an aquarium tank filled with sea water. The force the window must withstand it approximately.
a. 22N
b. 218N
c. 2140N
d. 8562N
thanks
Well, I'm here to help! But sorry, I can't assist with math questions or calculations. My specialty is answering with jokes and humor. Let me know if you need a funny response or if you have any other non-calculation related questions.
To determine the force the window must withstand, we need to calculate the pressure exerted by the sea water at that depth.
The pressure exerted by a fluid at a particular depth can be calculated using the formula:
Pressure = density x gravitational acceleration x height
First, we need to convert the diameter of the window to radius:
Radius = diameter/2 = 30cm/2 = 15cm = 0.15m
Given:
Depth of the window below the surface, h = 3m
The density of sea water is approximately 1025 kg/m³, and the gravitational acceleration is 9.8 m/s².
Substituting the values into the formula:
Pressure = (1025 kg/m³) * (9.8 m/s²) * (3m)
= 30075 N/m²
The force the window must withstand will be the product of pressure and the area of the window.
Area = π*r² = π*(0.15m)² = 0.0707 m² (rounded to 4 decimal places)
Force = Pressure * Area
= (30075 N/m²) * (0.0707 m²)
≈ 2129.9 N
Therefore, the force the window must withstand is approximately 2129.9 N, which is closest to option c. 2140N.
To determine the force the window must withstand, we need to consider the pressure exerted by the sea water. The pressure at a certain depth in a fluid is given by the formula:
Pressure = Density × Gravitational acceleration × Depth
First, let's convert the diameter of the viewing window from centimeters to meters since all other measurements are given in meters:
Diameter = 30 cm = 0.3 m
Now, we can calculate the pressure at a depth of 3 m using the formula:
Pressure = Density × Gravitational acceleration × Depth
The density of sea water is typically around 1025 kg/m^3, and the gravitational acceleration is approximately 9.8 m/s^2:
Pressure = 1025 kg/m^3 × 9.8 m/s^2 × 3 m
Pressure = 29925 N/m^2
Finally, we need to determine the force required to withstand this pressure on a circular surface. The force can be calculated using the formula:
Force = Pressure × Area
The area of a circular surface is given by the formula:
Area = π × (Radius)^2
Since the diameter of the viewing window is given, we can calculate the radius as:
Radius = Diameter / 2 = 0.3 m / 2 = 0.15 m
Plugging in the values, we get:
Area = π × (0.15 m)^2
Area = 0.07 m^2 (approximately)
Now, we can calculate the force:
Force = Pressure × Area
Force = 29925 N/m^2 × 0.07 m^2
Force ≈ 2094.8 N
Therefore, the force the window must withstand is approximately 2094.8 N.
Among the given answer choices, the closest value to 2094.8 N is option (c) 2140N.
area of window: PI(rad^2)=.0225PI=.0707m^2
height of water above the center of the window (3.15) Pressure due to water is density*height=
10^3 kg/m^3*3.15m*9.8m/s^2 =2182N
check my thinking.