Fluid Mechanics Fluid mechanics deals with fluids and the forces acting on them. (NOTE: You might be thinking that liquids are the only fluids. Remember that gases and plasma are also considered fluids.)
To understand fluid mechanics, let us review the concept of PRESSURE. (Hopefully, you still remember the lesson on elasticity/stress..Fingers crossed!)
Pressure may be defined as force per unit area. In equation form, we say
P = F/A
The SI unit for pressure is N/m2 or Pascal (Pa).
You have probably tried diving or floating on water. If your eardrums could talk, they would say No to diving., especially if you try to dive deeper. Your eardrums experience greater pressure as you swim deeper. Why is that so? The weight of the water above you causes the pressure. In other words, liquid pressure depends on the depth of the liquid.
Another factor that affects liquid pressure is density. It feels different when you are submerged in seawater and in swimming pool. These 2 have different densities. Seawater exerts greater pressure compared to the water in a swimming pool. Thus, we can say that greater density corresponds to greater liquid pressure.
And so, we can write the equation for liquid pressure as
P = ῤgh
where P = pressure, ῤ = density, g = acceleration due to gravity and h = depth
Now, let us try to derive this equation. We know that
Volume (V) = Area x height V = Ah (Equation 1)
Mass (m) = Density x Volume m = ῤV (Equation 2)
Weight of the liquid (W) = mass x g W = mg (Equation 3)
W = mg = (ῤV)g = ῤ(Ah)g
Let us go back to our first equation.
P = F/A P = W/A P = ῤ(Ah)g/A
You can cancel A (area) in the equation. And so you are left with,
P = ῤgh
Now, consider the figure above. The bottom of the blue block experiences greater pressure than its top surface. Let us say that the fluid in the container is static. Therefore the forces acting on the block are balanced. (Recall PHYSICS 1!) We can say that,
∑F = 0 ∑F = Force at the bottom - Force on the top surface - W = 0 ∑F = F2 – F1 - mg = 0
Since F = PA, then,
P2A – P1A - mg = 0
Rearranging the equation, we have
P2A = P1A - mg P2A = P1A + ῤ(Ah)g
You can cancel A (area) in the equation. And you will have P2 = P1 + ῤhg
Watch the video below for more details about fluid mechanics. After watching the video, answer the conceptual questions that follow. Write your answers on a short bond paper.
Conceptual Questions:
1. Which exerts greater pressure on the floor - high heels or flat soles? Explain. 2. How can padding the handles of heavy plastic bags help reduce the pressure on your fingers? 3. Create a concept map/web about the topic discussed. (Lessons discussed in the video may be included.)