A spherical viewing port 1.5 m below static water with radius 1 m. Find magnitude direction and location of thrust on viewing port.?

Question

Answer

Thrust on a Spherical Viewing Port

1. Calculating the Magnitude of Thrust:
To calculate the magnitude of thrust on the viewing port, we can use the concept of hydrostatic pressure. The pressure at a depth of 1.5 m below water can be calculated using the formula:
$$ P = \rho \cdot g \cdot h $$
where:
- $ P $ = Pressure
- $ \rho $ = Density of water
- $ g $ = Acceleration due to gravity
- $ h $ = Depth

2. Calculating the Direction of Thrust:
The direction of thrust on the viewing port will be perpendicular to the surface of the port. Since the port is a sphere, the thrust will act radially inward towards the center of the sphere.

3. Location of Thrust:
The thrust will act at the centroid of the spherical viewing port, which is located at a distance of $ \frac{3}{4} $ of the radius from the bottom of the sphere. Therefore, the location of the thrust will be at a distance of 0.75 m from the bottom of the sphere.

In conclusion, the magnitude of the thrust on the viewing port can be calculated using the hydrostatic pressure formula, and the direction of thrust will be radially inward towards the center of the sphere. The location of the thrust will be at a distance of 0.75 m from the bottom of the sphere.

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