The flow of blood in large artery of anesthetised dog is diverted through a venturi meter . The wider part of the meter has a cross sectional area equal to that of the artery.
`A=8mm^(2)` . The narrower part has an area
`a=4mm^(2)`. The narrower part has an area `a=4mm^(2)`. The pressure drop in the artery is 24 Pa . What is the speed of the blood in the artery ? `(1.60xx10^(3)kgm^(-3))`

Explanation

Area of wider part of venturi meter `A=8mm^(2)`
`=8xx10^(-6)m^(2)`
Area of narrower part `a=4mm^(2)=4xx10^(-6)m^(2)`
Decrease in pressure `P_(1)-P_(2)=24Pa`
From the equation of venturi meter,
`P_(1)-P_(2)=(1)/(2)rhov_(1)^(2)[((A)/(a))^(2)-1]`
`therefore2(P_(1)-P_(2))=rhov_(1)^(2)[((8)/(4))^(2)-1]`
`therefore2xx24=v_(1)^(2)xx(4-1)xxrho`
`thereforev_(1)^(2)=(48)/(3xxrho)=(16)/(rho)`
`thereforev_(1)^(2)=(16)/(1.06xx10^(3))=15.094xx10^(-3)=150.94xx10^(-4)`
`thereforev_(1)=12.285xx10^(-2)`
`thereforev_(1)=0.123m//s`