/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 An IV is connected to a patient'... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 22

An IV is connected to a patient's vein. The blood pressure in the vein has a gauge pressure of \(12 \mathrm{mm}\) Hg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV has the same density as blood.

Short Answer

Expert verified
Answer: The IV bag must be hung at a minimum height of 0.151 meters (or 15.1 cm) above the vein for the fluid to flow into the patient's vein.

Step by step solution

01

Identify the given information

The gauge pressure in the patient's vein is 12 mm Hg. We also know that the density of blood is approximately the same as the fluid in the IV.
02

Convert the pressure

To make the calculation easier, let's convert the gauge pressure from mm Hg to Pascals (Pa). We can use the conversion: 1 mm Hg = 133.3 Pa. Therefore, the gauge pressure in the vein is: \(12 \mathrm{mm}\,\mathrm{Hg} \times 133.3\,\mathrm{Pa/mm}\,\mathrm{Hg} = 1599.6 \, \mathrm{Pa}\)
03

Apply Pascal's Law and the concept of pressure in a fluid column

According to Pascal's law, the pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid. Therefore, we can say: \(P_{fluid} = P_{vein}\). The pressure in a fluid column is given by the hydrostatic pressure equation: \(P = h\rho g\), where \(h\) is the height of the liquid column, \(\rho\) is the density, and \(g\) is the acceleration due to gravity.
04

Solve for height h

Since \(P_{fluid} = P_{vein}\), we can write the equation as: \(h\rho g = P_{vein}\). Now we have to solve for the height (h) at which the IV bag must be hung: \(h = \dfrac{P_{vein}}{\rho g}\) The density of blood (and IV fluid) is 1060 kg/m鲁. The acceleration due to gravity is approximately 9.81 m/s虏.
05

Calculate the height

Now we can use the values we obtained to calculate the minimum distance above the vein: \(h = \dfrac{1599.6\,\mathrm{Pa}}{ 1060\,\mathrm{kg/m^{3}} \cdot 9.81\,\mathrm{m/s^2}} \approx 0.151\,\mathrm{m}\) So, the IV bag must be hung at least 0.151 meters (or 15.1 cm) above the vein for fluid to flow into the vein.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

At the surface of a freshwater lake the air pressure is 1.0 atm. At what depth under water in the lake is the water pressure 4.0 atm?

A block of aluminum that has dimensions \(2.00 \mathrm{cm}\) by \(3.00 \mathrm{cm}\) by \(5.00 \mathrm{cm}\) is suspended from a spring scale. (a) What is the weight of the block? (b) What is the scale reading when the block is submerged in oil with a density of \(850 \mathrm{kg} / \mathrm{m}^{3} ?\)
A container is filled with gas at a pressure of $4.0 \times 10^{5} \mathrm{Pa}\( The container is a cube, \)0.10 \mathrm{m}$ on a side, with one side facing south. What is the magnitude and direction of the force on the south side of the container due to the gas inside?
A cube that is \(4.00 \mathrm{cm}\) on a side and of density $8.00 \times 10^{2} \mathrm{kg} / \mathrm{m}^{3}$ is attached to one end of a spring. The other end of the spring is attached to the base of a beaker. When the beaker is filled with water until the entire cube is submerged, the spring is stretched by \(1.00 \mathrm{cm} .\) What is the spring constant?

Two identical spheres are dropped into two different columns: one column contains a liquid of viscosity \(0.5 \mathrm{Pa} \cdot \mathrm{s},\) while the other contains a liquid of the same density but unknown viscosity. The sedimentation velocity in the second tube is \(20 \%\) higher than the sedimentation velocity in the first tube. What is the viscosity of the second liquid?
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Classical Mechanics

Read Explanation

Nuclear Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Physics of Motion

Read Explanation

Geometrical and Physical Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.