Question

Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.83m. The density of blood is$\mathbf{1}\mathbf{.}\mathbf{06}\mathbf{\times }\mathbf{10}\mathbf{}\mathit{k}\mathit{g}\mathbf{/}{\mathit{m}}^{\mathbf{3}}$.

Short answer

Hydrostatic pressure difference in blood pressure between the brain and foot is$1.90\times {10}^{4}Pa$

Step-by-step solution

The given data

1. Density of blood is$p=1.06\times {10}^{3}kg/m^3$
2. Height of person$h=1.83m$

Understanding the concept of hydrostatic pressure difference

We can use the formula for hydrostatic pressure in terms of density, gravitational acceleration, and height to solve for pressure difference.Hydrostatic pressure is that, which is exerted by a fluid at any point of time at equilibrium due to the force applied by gravity.

Formula:

Net pressure applied on a fluid surface, $∆p=pgh$ (i)

Calculation of net hydrostatic pressure

Hydrostatic pressure difference in blood pressure between the brain and foot using equation (i) and the given values can be written as:

$$\begin{gathered} ∆p=1.06\times {10}^3\times 9.8\times 1.83 \\ =1.90\times {10}^{4}Pa \end{gathered}$$

Hence, the value of hydrostatic difference in pressure is$1.90\times {10}^{4}Pa$