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Chapter 1: Q11E (page 391)

In intravenous feeding, a needle is inserted in a vein in the patient’s arm and a tube leads from the needle to a reservoir of fluid (density 1050 kg/m3) located at height h above the arm. The top of the reservoir is open to the air. If the gauge pressure inside the vein is 5980 Pa, what is the minimum value of h that allows fluid to enter the vein? Assume the needle diameter is large enough that you can ignore the viscosity (see Section 12.6) of the fluid.

Short Answer

Expert verified

The minimum value of height h is 0.58 m .

Step by step solution

01

Given Data

The height above the arm is h.

The gauge pressure inside the vein is P=5980Pa.

The density of fluid is ρ=1050kg/m3.

02

Understanding the gauge pressure

In this problem, the relation of gauge pressure will be applied to calculate the minimum height that allows fluid to enter the vein.

03

Determining the height

The relation of gauge pressure can be written as:

P=ρgh

Here, g is the gravitational acceleration.

Substitute 5980 Pa for P,1050kg/m3for ρ, and9.80m/s2forg in the above relation.

5980Pa=1050kg/m39.80m/s2hh=0.58m

Thus, the required height is h=0.58m.

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