That is, we need to find the integral $\int_0^h 62.4x(y)dy \cdot h$. To find the total fluid force on the vertical side of the tank, we need to integrate this expression over the entire height of the tank. So, the fluid force on this strip is $62.4x(y)dy \cdot h$.ĥ. The volume of the water above the strip is $x(y)dy \cdot h$, and the weight-density of water is 62.4 pounds per cubic foot. The fluid force on this strip is equal to the weight of the water above it. Assume that the tank is full of water (The weight-density of water is 62.4 pounds per cubic foet. The width of this strip is $dy$, and its length is a function of $y$. O My Notes Ask Your Teacher Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Now, we need to find the fluid force on a small horizontal strip of the vertical side of the tank. Since the tank is full of water, the depth will vary linearly from 0 at the top to the height of the tank at the bottom.ģ. Math Calculus Calculus questions and answers Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Next, we need to find the depth of the water at any point on the vertical side of the tank. The formula for the area of a trapezoid is $A = \frac(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height.Ģ. First, we need to find the area of the trapezoid. For example, suppose that in a setting similar to the problem posed in Preview Activity 6.1. What is the meaning of the value you find? Why?īecause work is calculated by the rule \( W = F \cdot d\), whenever the force \( F\) is constant, it follows that we can use a definite integral to compute the work accomplished by a varying force. Fluid Force: Fluid is a substance which continuously flows unless contained and exerted upon an outside. At 30 feet below sea level the pressure is 30 pounds per square inch. At sea level the atmospheric pressure is 15 pounds per square inch. It is measured in pounds per square inch or kilograms per square centimeter. Evaluate the definite integral \( \int^50_0 B(h) dh\). Note: The density of water is 62.4 lbs per cubic foot. Figure 7.7.1 Pressure is the force on a body's surface area.= B(h)\Delta h\) measure for a given value of \( h\) and a small positive value of \( \Delta h\)?
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