To explain: How to approximate to force against the end of the tank by the Riemann sum.
Answer to Problem 14E
The answer is:
Explanation of Solution
Given information:
The vertical end of the tank contained water weight
The figure is:
Calculation:
Let's first review the equation for a fluid force in a constant-depth surface in order to determine the force acting against the end of the tank.
Where,
in order to approximate the force using Riemann sum, let divide the height of the of the tank into
Now assume that the centre of the semi-ellipse is
Put the tank in the plane of cartesian coordinates will allow us to draw one strip as seen below.
Where,
Now, The Riemann sum formula for the force is given below.
To generate the force approximation, substitute the value from the graph into equation
To find: The force as an integral.
Answer to Problem 14E
The answer:
Explanation of Solution
Given information:
The vertical end of the tank contained water weight
The figure is:
Calculation:
Have a look at the graph above. The y-axis of the graph is symmetric, as can be seen. multiply by two and integrate the right side using the same strip. Put the integral together,
Now let,
New boundaries of
Upper boundary:
Lower boundary:
Put everything to the integration:
Now evaluate the integral:
Therefore, the required force as an integral is
Chapter 7 Solutions
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