Question

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 $\mathbf{100}$ to$\mathbf{200}\mathbf{\text{mm}}$of ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}$above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of millimeters of ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}$because body fluids, including the cerebrospinal fluid, typically have the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap as illustrated in Figure P14.20. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed. If the fluid rises to a height of $\mathbf{\text{160mm}}$, we write its gauge pressure as$\mathbf{\text{160mm}}$ ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}$. (a) Express this pressure in Pascal’s, in atmospheres, and in millimeters of mercury. (b) Some conditions that block or inhibit the flow of cerebrospinal fluid can be investigated by means of Queckenstedt’s test. In this procedure, the veins in the patient’s neck are compressed to make the blood pressure rise in the brain, which in turn should be transmitted to the cerebrospinal fluid. Explain how the level of fluid in the spinal tap can be used as a diagnostic tool for the condition of the patient’s spine.

Short answer

(a) The pressure, in Pascal’s $\text{1.57kPa}$, in atmospheres $P-P_0=0.01\text{55atm}$, and in millimeters of mercury $\text{11.8mm}$.

(b) Blockage of the fluid within the spinal column or between the skull and the spinal column would prevent the fluid level from rising.

Step-by-step solution

Pressure:

Pascal’s law states that when pressure is applied to an enclosed fluid, the pressure is transmitted undiminished to every point in the fluid and to every point on the walls of the container.

The pressure in a fluid at rest varies with depth in the fluid according to the expression

$\mathit{P}\mathbf{=}{\mathit{P}}_{\mathbf{0}}\mathbf{+}\mathit{\rho }\mathit{g}\mathit{h}$

Where,${\mathit{P}}_{\mathbf{0}}$is the pressure at$\mathit{h}\mathbf{=}\mathbf{0}$and$\mathit{\rho }$is the density of the fluid, assumed uniform.

(a) Pressure in Pascal’s, in atmospheres, and in millimeters of mercury:

From step (1), you have

$P=P_0+\rho gh$

And the gauge pressure is,

$\begin{array}{rcl}P-P_0& =& \rho gh\\ & =& (100\text{0kg}/{\text{m}}^{\text{3}})(9.\text{8m}/{\text{s}}^{\text{2}})(0.160\text{m})\\ & =& 1.5\text{7kPa}\\ & =& 1.57\times {10}^3\text{Pa}\left(\frac{\text{1atm}}{1.013\times {10}^{\text{3}}\text{Pa}}\right)\end{array}$

$P-P_0=0.015\text{5atm}$

It would lift a mercury column to height,

$\begin{array}{rcl}h& =& \frac{P-P_0}{\rho g}\\ & =& \frac{156\text{8Pa}}{(1360\text{0kg}/{\text{m}}^{\text{3}})(9.\text{8m}/{\text{s}}^{\text{2}})}\\ & =& 11.8\text{mm}\end{array}$

(b) The level of fluid in the spinal tap:

Blockage of the fluid within the spinal column or between the skull and the spinal column would prevent the fluid level from rising.