Question

The figure shows a water-filled syringe with a 4.0-cm-long needle. What is the gauge pressure of the water at the point P, where the needle meets the wider chamber of the syringe? The viscosity of water is 1.0×10-3Pa ∙ s.

Answer 1

Answer:

Pressure at P point is given as

$P_p = 1.042 \times 10^5 Pa$

Explanation:

As we know by poiseuille's equation of viscous flow of liquid through cylindrical pipe

$Q = \frac{\Delta P \pi r^4}{8\eta L}$

here we know that

L = 4 cm

$\eta = 1 \times 10^{-3} Pa s$

r = 1 mm

Q = flow rate

$\pi r^2 v = \frac{\Delta P \pi r^4}{8\eta L}$

$v = \frac{\Delta P r^2}{8 \eta L}$

$10 = \frac{\Delta P (10^{-3})^2}{8(1 \times 10^[-3})(0.04)}$

$3.2 \times 10^{-3} = \Delta P (10^{-6})$

$\Delta P = 3.2 \times 10^3 Pa$

now we have

$P_p - P_{atm} = 3.2 \times 10^3$

$P_p = 1.01 \times 10^5 + 3.2 \times 10^3$

$P_p = 1.042 \times 10^5 Pa$