The arterioles (small arteries) leading to an organ, constrict in order to decrease flow to the organ. To shut down an organ, blood flow is reduced naturally to 2.80% of its original value. By what factor did the radii of the arterioles constrict? Penguins do this when they stand on ice to reduce the blood flow to their feet.

Respuesta :

Answer:

The main factor that causes vasoconstriction is the high concentration calcium inside muscle cells.

Explanation:

When the vessels suffer vasoconstriction, the blood supply is decreased and in this way the heat of the body is maintained. The way this happens is because the blood can no longer reach the surface and therefore decreases outward heat radiation.  The main factor that causes vasoconstriction is the high concentration calcium inside muscle cells. There are several factors that cause vasoconstriction, internal or external. Environment is one of the external factors, and what happens to the penguins' feet is an example for it, since they are trying to preserve body heat to survive.

The final radii of the arteriole is reduced by the factor of 0.409 after the constriction of the arteriole.

The flow rate is defined as the amount of fluid flow through the artery in the given time period at the cross-sectional area.

Computation for the radii of constricted arterioles

The flow rate for the artery is given by:

[tex]Q_1=\dfrac{\pi Pr^4}{8\eta l}[/tex]

Where, P is the pressure, r is the radius, [tex]\eta[/tex] is the viscosity, and l is the length.

The value of flow rate is reduced to 2.80 % of its natural values. The reduced flow rate is given as:

[tex]Q_2=Q_1\;\times\;\dfrac{2.80}{100} \\Q_2=0.028Q_1[/tex]

The ratio of the flow rate is given as:

[tex]\dfrac{Q_2}{Q_1} =\dfrac{r_f^4}{r_i^4}\\\\ \dfrac{0.028\;Q_1}{Q_1} =\dfrac{r_f^4}{r_i^4}\\\\0.028\;r_f^4=r_i^4\\\\r_i=0.409r_f[/tex]

The final radii of the arteriole is reduced by the factor of 0.409 after the constriction of the arteriole.

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