Consider the flow of blood, whose density is `1.06 xx 10^3 kgm^(-3)`, in a large artery of an anesthetised Alsatian which is diverted through a venturi meter. The area of cross-section of both the wider part of the meter and that of the artery is `12 mm^(2)` and the narrower part has an area of `6 mm^(2)`. If the pressure drop in the artery is 20 Pa, then the speed of the blood in the artery is `1.10 xx 10^(-x) m//s`. Now, what is x = ? (Take the density of the blood is )

Answer

`01.00`

Explanation

Speed of the fluid through the wide neck is-
`v = sqrt((2(P_(1)-P_(2)))/rho) {(A/a)^(2) - 1}^(-1/2)`
As `A/a = 12/6 = 2`
`therefore v = sqrt((2 xx 20)/(1060 (2^(2)-1))) = 1/sqrt(79.5) ~~ 1/9 ~~ 1.11 xx 10^(-1)`
Comparing with given value,
`x = 1`