Chapter 9, Problem 83AP

The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H₂O above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of mm of H₂O because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height lo which the fluid rises is observed, as shown in Figure P9.83. If the fluid ruses to a height of 160. mm, we write its gauge pressure as 160. mm H₂O. (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions ran be investigated by means of the Queckensted test. In this procedure, the veins in the patient’s neck are compressed lo make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the level of the fluid. What might account for this phenomenon?

To determine

The pressure of the mercury in terms of Pascal’s, in atmospheres, and in millimeters of mercury.

Answer to Problem 83AP

The pressure of the mercury in terms of Pascal’s is $1.5\text{7}\text{kPa}$, in terms of atmospheres is $1.55\times {10}^{-2}\text{Pa}$, and in terms of millimeters of mercury is $11.\text{8}\text{mm}\text{of}\text{Hg}$.

Explanation of Solution

Given Info: Gauge pressure is $160{\text{mmH}}_{\text{2}}\text{O}$ and Density of the water ${\rho }_{{\text{H}}_{\text{2}}\text{O}}$ is ${10}^3\text{kg}/{\text{m}}^{\text{3}}$, Density of the mercury ${\rho }_{\text{Hg}}$ is $13.6\times {10}^3\text{kg}/{\text{m}}^{\text{3}}$.

Formula to calculate pressure of the mercury in terms of Pascal’s is,

$P_{\text{pascals}}=g\cdot G_{\text{p}}\cdot {\rho }_{{\text{H}}_{\text{2}}\text{O}}$

• $P_{\text{pascals}}$ is the pressure of the mercury,
• ${\rho }_{{\text{H}}_{\text{2}}\text{O}}$ is the density of the water,
• $G_{\text{p}}$ is the gauge pressure,
• g is the  acceleration due to gravity.

Substitute ${10}^3\text{kg}/{\text{m}}^{\text{3}}$ for ${\rho }_{{\text{H}}_{\text{2}}\text{O}}$, $9.8\text{m}/{\text{s}}^{\text{2}}$ for g and $160{\text{mmH}}_{\text{2}}\text{O}$ for $G_{\text{p}}$ to find $P_{\text{pascals}}$ ,

$\begin{array}{c}{P}_{\text{pascals}}=\left({10}^3\text{kg}/{\text{m}}^{\text{3}}\right)\left(9.8\text{m}/{\text{s}}^{\text{2}}\right)\left(160\text{mm}\right)\left(\frac{1\text{m}}{{10}^3\text{mm}}\right)\\ =\left(1568\text{Pa}\right)\left(\frac{1\text{kPa}}{{10}^3\text{Pa}}\right)\\ \approx 1.57\text{kPa}\end{array}$

Formula to calculate pressure of the mercury in terms of atmospheres is,

$P_{\text{atm}}=P_{\text{pascals}}\frac{1\text{atm}}{\left(1.013\times {10}^5\text{Pa}\right)}$

• $P_{\text{pascals}}$ is the pressure of the mercury in terms of Pascal’s,
• $P_{\text{atm}}$ is the pressure of the mercury in terms of atmospheres,

Substitute $1.5\text{7}\text{kPa}$ for $P_{\text{pascals}}$ to find $P_{\text{atm}}$,

$\begin{array}{c}{P}_{\text{atm}}=1.5\text{7}\text{kPa}\left(\frac{{10}^3\text{Pa}}{1\text{kPa}}\right)\left(\frac{1\text{atm}}{\left(1.013\times {10}^5\text{Pa}\right)}\right)\\ =0.0155\text{atm}\\ \approx 1.55\times {10}^{-2}\text{atm}\end{array}$

Formula to calculate pressure of the mercury in terms of millimeters of mercury is,

$P_{\text{mm}\text{of}\text{hg}}=\left(\frac{{\rho }_{{\text{H}}_{\text{2}}\text{O}}}{{\rho }_{\text{Hg}}}\right)G_{\text{p}}$

• ${\rho }_{{\text{H}}_{\text{2}}\text{O}}$ is the density of the water,
• $G_{\text{p}}$ is the gauge pressure,
• ${\rho }_{\text{Hg}}$ is the density of the mercury,
• $P_{\text{mm}\text{of}\text{hg}}$ is the pressure of the mercury in terms of millimeters of mercury,

Substitute ${10}^3\text{kg}/{\text{m}}^{\text{3}}$ for ${\rho }_{{\text{H}}_{\text{2}}\text{O}}$, $13.6\times {10}^3\text{kg}/{\text{m}}^{\text{3}}$ for ${\rho }_{\text{Hg}}$ and $160{\text{mmH}}_{\text{2}}\text{O}$ for to find $P_{\text{mm}\text{of}\text{hg}}$,

$\begin{array}{c}{P}_{\text{mm}\text{of}\text{hg}}=\left(\frac{{10}^3\text{kg}/{\text{m}}^{\text{3}}}{13.6\times {10}^3\text{kg}/{\text{m}}^{\text{3}}}\right)\left(160{\text{mmH}}_{\text{2}}\text{O}\right)\left(\frac{1\text{m}}{{10}^3\text{mm}}\right)\\ =\left(\frac{{10}^3\text{kg}/{\text{m}}^{\text{3}}}{13.6\times {10}^3\text{kg}/{\text{m}}^{\text{3}}}\right)\left(160\times {10}^{-3}\text{m}\right)\\ =0.01176\text{m}\text{of}\text{Hg}\left(\frac{1\text{mm}}{{10}^{-3}\text{m}}\right)\\ \approx 11.\text{8}\text{mm}\text{of}\text{Hg}\end{array}$

Conclusion:

The pressure of the mercury in terms of Pascal’s is $1.5\text{7}\text{kPa}$, in terms of atmospheres is $1.55\times {10}^{-2}\text{Pa}$, and in terms of millimeters of mercury is $11.\text{8}\text{mm}\text{of}\text{Hg}$.

To determine

The normal effect on the height of the fluid in the spinal tap.

Explanation of Solution

The spinal tap is the process in which a hollow tube is inserted in the spinal cord and the rise in the pressure leads to the cerebrospinal fluid to rise in the tube to some height in the tube. This process of measuring the height in the tube is called the spinal tap.

The effect on the spinal tap if the liquid undergoes some pressure and when we insert some hollow tube immersed in it, the pressured liquid enter into the tube to certain height depends upon the pressure that the liquid is exhibiting, that is due to the converging of volume of the surface from larger volume to smaller volume the cerebrospinal fluid will increase in the tube.

Conclusion: This measure of the increase in the height of the liquid in the tube can be used to know the level of the cerebrospinal fluid.

To determine

the compressing the veins had no effect on the level of the fluid.

Explanation of Solution

The cerebrospinal fluid does not raise in the tube by normal effect means in that case test has been made by the physician and it is called as Queckensted test.

The test sates that if the liquid does not rise, then physician manually compress the nerves around the neck, this cause to increase the pressure in the body and liquid raises. In that case also the liquid is not raising up means then it leads to some obstruction is there in the pathway of the liquid.

Conclusion:

The obstruction can be of some tumor growth or the any other parts can be damaged.