Answer:
Taking into account that:
The flow velocity u of a fluid is a vector field
u = u (x, t)
What gives the velocity of a Fluid Plot at position x y time t.
q = || u ||
Now if the flow is continuous as it happens in the blood vessels then:
The flow of a fluid is said to be constant if it does not move over time, that is why the variant would be 0.
Explanation:
As for the pump with narrow vessels, there the area would be less, therefore the flow also and the flow velocity as well. Adding that the friction with the walls increases as it is narrower, thus generating an increase in pressure with the flow of the liquid.
So this is where we have to put emphasis on the biophysics branch that explains the following:
The Venturi effect is explained by the Bernoulli Principle and the principle of continuity of mass. If the flow rate of a fluid is constant but the section decreases, the speed necessarily increases after crossing this section. By the theorem of conservation of mechanical energy, if the kinetic energy increases, the energy determined by the value of pressure necessarily decreases.
Indeed, according to Bernoulli's principle:
P 1 + 21 ρv 12 + ρgh 1 = P 2 + 21 ρv 22 + ρgh 2
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