# Calcluated density value different from literature

## Homework Statement

A blood pressure cuff is used to measure the gage pressure associated with blood flow in the body. “Normal”, systolic blood pressure is commonly reported as 120 mm of mercury. This value represents the vertical displacement of mercury (h) resulting from the gage pressure within the device. (The density of mercury is ρ = 1.38 x 10^4 x kg/m^3 )

a. Calculate the gage pressure within the device (in Pa) that corresponds to a vertical displacement of 120 mmHg.

b. The fluid in the device is replaced with a glycerin solution and the gage pressure from part b is applied. The displacement in the column corresponding to this gage pressure is 166 mm of glycerin. What is the density of this glycerin solution?

Pgage= ρ*g*h

## The Attempt at a Solution

a) Pgage= ρ*g*h = (1.38 x 10^4 kg/m^3)*(9.8 m/s^2)*(120mm)* (1m/1000mm)
Pgage=16200 kPa
b) ρglycerin=Pgage= 16200Pa/[(9.8 m/s^2)*(166mm)*(1m/1000mm)
ρglycerin=9960 kg/m^3 which is different from the density of glycerin in literature (1250 kg/m^3)

So I am wondering these calculations are right or if I am missing something.
Thanks!

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

A blood pressure cuff is used to measure the gage pressure associated with blood flow in the body. “Normal”, systolic blood pressure is commonly reported as 120 mm of mercury. This value represents the vertical displacement of mercury (h) resulting from the gage pressure within the device. (The density of mercury is ρ = 1.38 x 10^4 x kg/m^3 )

a. Calculate the gage pressure within the device (in Pa) that corresponds to a vertical displacement of 120 mmHg.

b. The fluid in the device is replaced with a glycerin solution and the gage pressure from part b is applied. The displacement in the column corresponding to this gage pressure is 166 mm of glycerin. What is the density of this glycerin solution?

Pgage= ρ*g*h

## The Attempt at a Solution

a) Pgage= ρ*g*h = (1.38 x 10^4 kg/m^3)*(9.8 m/s^2)*(120mm)* (1m/1000mm)
Pgage=16200 kPa
b) ρglycerin=Pgage= 16200Pa/[(9.8 m/s^2)*(166mm)*(1m/1000mm)
ρglycerin=9960 kg/m^3 which is different from the density of glycerin in literature (1250 kg/m^3)

So I am wondering these calculations are right or if I am missing something.
Thanks!

The height of the column is inversely proportional to the density of the fluid, so your answer appears to be consistent with the data given. I agree with you that the glycerin solution is unrealistically dense.