Question

The maximum blood pressure in the upper arm of a healthy person is about 120mmHg (gage pressure). If a vertical tube open to the atmosphere is connected to the vein in the arm of the person, determine how high the blood will rise in the tube. Take the density of human blood to be 1060 kg=m3.

Answer 1

Height, the blood will rise in Tube=1.5396 m

Step-by-step explanation:

Given Data:

Maximum blood pressure in the upper arm=
`P_(blood)=120\ mmHg`

Density of human blood=
`\rho_(Blood)=1060\ kg/m^3`

g=9.8m/s^2

Density of mercury=
`\rho_(mercury)\\`≅13600 Kg/m^3 (From Internet)

Required:

Height, the blood will rise in Tube=?

Solution:

Pressure of blood=Pressure of mercury

`P_(blood)=P_(Mercury)\\\rho_(blood)*g*h_(blood)=\rho_(Mercury)*g*h_(Mercury)`

On rearranging the above Equation:

`h_(blood)=(\rho_(Mercury)*g*h_(Mercury))/(\rho_(blood)*g) \\h_(blood)=(\rho_(Mercury)* h_(Mercury))/(\rho_(blood))\\`

`h_(Mercury)=0.12 m (From\ 120\ mmHg)`

`h_(blood)=(13600*0.12)/(1060) \\h_(blood)=1.5396\ m`

Height, the blood will rise in Tube=1.5396 m