Name: Density of Substances
Uploaded: 2019-07-19
Duration: 6 min 34 s
Description: What is the density of a substance? Density is a very important thing to understand but is a bit tricky. Let’s fully grasp the idea of density from this video.

Question

A Gipsy car has a canvas top. When the car runs at high speed, the top bulges out. Explain.

Accepted Answer

Bernoulli's equation relates the speed of a fluid $(ν)$ and the pressure $(P)$ and the height $(h)$ at that point above a reference level.
The fluid should be incompressible, non-viscous and in irrotational flow. This principle is based on the conservation of energy.
According to this principle,
$P + ρ g h + \frac{1}{2} ρ v^{2} = constant$

Applying this principle in a moving vehicle, as shown in the below diagram,

Let there be two points: point $1$ (just above the canvas of the Gipsy) and the point $2$ (just below the canvas of the Gipsy). Then,

$P_{1} + ρ g h_{1} + \frac{1}{2} ρ ν_{1}^{2} = P_{2} + ρ g h_{2} + \frac{1}{2} ρ ν_{2}^{2}$ ,

where symbols have their usual meanings.
As both the points are at the nearly equal height, so $h_{1} = h_{2}$ .

Then the equation becomes,
$P_{1} + \frac{1}{2} ρ ν_{1}^{2} = P_{2} + \frac{1}{2} ρ ν_{2}^{2}$
When the Gipsy moves, the air above the canvas also moves faster than that at the below of the canvas, i.e., $ν_{1} > ν_{2}$ .

So from the equation, we can conclude that the pressure above the canvas is lesser than that below the canvas, i.e., $P_{1} < P_{2}$ .
Due to this pressure difference, there is a force developed from higher pressure (below the canvas) to the lower pressure (above the canvas) region, so the canvas bulges out.

A Gipsy car has a canvas top. When the car runs at high speed, the top bulges out. Explain.

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