# Problem:  An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.14 cm3/s through a needle of radius 0.185 mm and length 2.3 cm. The gauge pressure of the blood in the patient's vein is 8.00 mm Hg. (Assume the viscosity of saline solution is the same as water and the temperature is 20°C) p = 1025kg/m3A) Calculate the gauge pressure created at a depth of 1.75 m in a saline solution, assuming its density to be that of sea water.B)  Calculate the new flow rate if the height of the saline solution is decreased to 1.05 m in cm3/s. The viscosity of water is 0.001002 Pa • s.C)  At what height would the direction of flow be reversed in cm?C) At what height would the direction of flow be reversed in cm?

###### FREE Expert Solution

Gauge pressure:

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{h}}{\mathbf{\rho }}{\mathbf{g}}}$

Poiseuille’s law:

$\overline{){\mathbf{Q}}{\mathbf{=}}\frac{\mathbf{\pi }\mathbf{∆}\mathbf{P}{\mathbf{r}}^{\mathbf{4}}}{\mathbf{8}\mathbf{\eta }\mathbf{l}}}$, where Q is the flow rate, P is pressure, r is the radius, η is fluid viscosity, and l is the length of tubing.

A)

From the gauge pressure equation, h is the depth (1.75 m), ρ is the density of saline water (1025 kg/m3), and g is 9.81 m/s2

we have:

P = (1.75)(1025)(9.81) = 1.76 × 104 N/m2

The gauge pressure created at a depth of 1.75 m in a saline solution is 1.76 × 104 N/m2. ###### Problem Details

An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.14 cm3/s through a needle of radius 0.185 mm and length 2.3 cm. The gauge pressure of the blood in the patient's vein is 8.00 mm Hg. (Assume the viscosity of saline solution is the same as water and the temperature is 20°C) p = 1025kg/m3

A) Calculate the gauge pressure created at a depth of 1.75 m in a saline solution, assuming its density to be that of sea water.

B)  Calculate the new flow rate if the height of the saline solution is decreased to 1.05 m in cm3/s. The viscosity of water is 0.001002 Pa • s.

C)  At what height would the direction of flow be reversed in cm?

C) At what height would the direction of flow be reversed in cm?