2.2. Example Problem: Determining Pressure at Bottom of Tank

So, we have a 6 meter deep tank, so this is 6 meter, right? And contains 4 meters of water, so this is as it is written here very clear 4 meter and 2 meter of oil of relative density 0.88.

In this section, we are introduced to a specific problem related to fluid mechanics. We have a tank that is 6 meters deep. Within this tank, there are layers of different fluids: there are 4 meters of water and 2 meters of oil having a relative density (or specific gravity) of 0.88. The relative density helps us understand how the density of the oil compares to the density of water, which is an essential property in fluid mechanics.

Think of a glass filled with different colored liquids. The heavier liquid settles at the bottom, while the lighter one floats on top. Just like the oil floating on the top of the water in this tank, understanding how these different liquids interact helps us comprehend concepts such as pressure and buoyancy.

First, determine the pressure while water interface, that is, p2, so p2 is written as p1 plus pressure due to 2 meters of oil, very nice. So or p1 plus what is the pressure due to 2 meters of oil, gamma 0 into 2.

To find the pressure at the interface between the water and the oil (denoted as p2), we need to consider the pressure exerted by the oil. The pressure p2 can be calculated by starting from the known pressure at the top of the oil layer (p1, which is 0 at the open tank surface) and adding the pressure created by the 2 meters of oil above that point. This is calculated using the formula: pressure = density × gravitational acceleration × height (p = ρgh).

Imagine pressing down on a full balloon filled with water; the pressure you feel at the bottom of the balloon increases as you apply more force. Similarly, in our tank, the weight of the oil above pushes down on water below, increasing the pressure at the interface.

Here p1 is equal to 0, right? Whereas gamma not which is the pressure of the oil it is 0.88 specific gravity into 9790 that is 8615.2 Newton per meter square.

In calculating p2, we substitute our known value of p1 (which is 0) and calculate the pressure due to the 2 meters of oil (using its specific gravity relative to water). The unit weight (gamma) of the oil is calculated to understand how much pressure it exerts on the underlying water layer. The calculation provides us with a specific value in Newtons per square meter, which reflects the amount of force being applied over any given area.

Consider the way we use scales to measure weight. Just as an object of known weight can exert a certain force on the scale, the heavy oil presses down on the water below, creating pressure—this is part of the foundation of how we measure force and pressure in fluids.

So p3 will be p2 + pressure due to 4 meters of water, right.

After calculating p2 (the pressure at the bottom of the oil layer), the next step involves calculating p3, which is the pressure at the bottom of the tank. To do this, we add the pressure contribution from the 4 meters of water above the interface. This cumulative approach helps us determine the total pressure acting at the bottom of the tank, incorporating contributions from all fluid layers above.

Think of layers in a cake, where each layer adds to the overall height and weight of the cake. Similarly, the water layer contributes to the total pressure felt at the bottom of the tank. Each layer influences the pressure just like each cake layer affects the cake's weight.

The answer was P 3 is equal to 56.39 kilo Pascal.

After performing all necessary calculations, we arrive at the final result for p3, which is the pressure at the bottom of the tank. Expressed as 56.39 kilopascals, this pressure is a crucial parameter for engineers when designing tanks and systems to ensure that structures can handle the weight of the fluids.

When filling a car tire, the pressure inside is measured in kilopascals (kPa). If the pressure is too low, the tire may not perform well; too high, and it could burst. Similarly, understanding the pressure at the tank's bottom is vital for ensuring safety and functionality in engineering applications.

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