A person of height $1.65 \mathrm{~m}$ is standing upright. The additional external force required by blood…

A person of height $1.65 \mathrm{~m}$ is standing upright. The additional external force required by blood vessel of length $1 \mathrm{~cm}$, diameter $1 \mathrm{~mm}$ at feet to balance the pressure compared to similar blood vessel in head is (Density of blood $=1.1 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$ )
  1. $0.57 \mathrm{~N}$
  2. $5.7 \mathrm{~N}$
  3. $1.85 \mathrm{~N}$
  4. $3.14 \mathrm{~N}$

Solution

Pressure difference $\Delta \mathrm{p}=\rho \mathrm{gh}$ and force exerted $ \begin{aligned} & \mathrm{F}=\Delta \mathrm{P} . \mathrm{A}=\rho \mathrm{gh} .2 \pi \mathrm{r}(\mathrm{r}+\mathrm{h}) \\ & =1.1 \times 10^3 \times 10 \times 1.65 \times 2 \times \frac{22}{7} \times 0.5 \times 10^{-3} \\ & \left(0.5 \times 10^{-3}+\mathrm{h}\right) \\ & =18150 \times 2 \times \frac{22}{7} \times 0.5 \times 10^{-3}\left(0.5 \times 10^{-3}+10 \times\right. \\ & \left.10^{-3}\right) \\ & \therefore \mathrm{F} \cong 0.57 \mathrm{~N} . \end{aligned} $

Asked in: AP EAMCET 2023 (15 May Shift 1)

Practice more Mechanical Properties of Fluids questions on Aicharya