Question

 glucose solution of density 1050 kg/m3 is transferred from a collapsible bag through a tube and syringe into the vein of a person's arm. The pressure in the arm exceeds the atmospheric pressure by 1400 N/m2.
How high above the arm must the top of the liquid in the bottle be so that the pressure in the glucose solution at the needle exceeds the pressure of the blood in the arm? Ignore the pressure drop across the needle and tubing due to viscous forces.

Answer 1

Answer:

$0.136$ meter

Explanation:

The following equation will be used to solve this question -

$P_{atm} + \frac{1}{2} (rho)v^2 + (rho)gh = P_{inject} + \frac{1}{2}(rho)v_{inject}^2 + (rho)gh_{injec}$

$P_{atm} -P_{injec} = 1400\frac{N}{m^{2} }$

Velocity is zero.

Removing out the nullified terms from the above equation, we get -

$(rho)gh = P_{injec}\\1050 * 9.8 * h = 1400\\h = \frac{1400}{1050*9.8} \\h = 0.136$ meter

Hence,  top of the liquid in the bottle must be at a height of $0.136$ meter.