AP Physics 2 Exam: Fluid Statics and Dynamics
Question:
A circular pipe with a diameter of 0.2 meters is inclined at an angle of 30 degrees with respect to the horizontal. The pipe is filled with water up to a height of 5 meters. Calculate the pressure exerted by the water on the bottom of the pipe.
Solution:
To calculate the pressure exerted by the water on the bottom of the pipe, we can use the equation for pressure:
Pressure = Density × gravitational acceleration × height
Calculate the density of water:
In SI units, the density of water is approximately 1000 kg/m³.
Calculate the gravitational acceleration:
The standard value for the acceleration due to gravity is 9.8 m/s².
Calculate the vertical height:
The vertical height can be calculated using the trigonometric relationship:
height = 5 meters × sin(30 degrees)
Now, let's substitute the values into the pressure equation:
Pressure = 1000 kg/m³ × 9.8 m/s² × (5 meters × sin(30 degrees))
Simplifying the expression:
Pressure = 1000 kg/m³ × 9.8 m/s² × (5 meters × 0.5)
Pressure = 1000 kg/m³ × 9.8 m/s² × 2.5 meters
Pressure = 24500 Pa
Therefore, the pressure exerted by the water on the bottom of the pipe is 24500 Pa.