10.13 Glycerin flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerin collected per second at one end is 4.0 * 10^–3 kg s^–1, what is the pressure difference between the two ends of the tube? (Density of glycerin = 1.3 * 10³ kg m^–3 and viscosity of glycerin = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct]. 

Surface tension is the force acting on the surface of the liquid.

Bernoulli's principle states that in a steady flow, the sum of pressure, kinetic energy per unit volume, and potential energy per unit volume remains constant.

Yes, the Mechanical properties of fluids class 11th physics is important in NEET. On average, 1-2 questions would be asked from this chapter, which you can cover from the Class 11th Mechanical Properties of Fluids notes.

The main mechanical properties of fluids are exerting pressure, resisting flow or viscosity, forming surface tension, following Bernoulli's principle, and moving in a streamline.

Since velocity does not change, so acceleration will be zero.

mg = FB + Fv $\Rightarrow \frac{4\pi }{3}{r}^3\rho g=\frac{4\pi }{3}{r}^3\sigma g+6\pi \eta rv$

$\Rightarrow v=\frac{2r^2\left(\rho -\sigma \right)g}{9\eta }=\frac{2\times 0.1\times 0.1\times 10^{-6}\times \left(10^4-10^3\right)\times 10}{9\times 1.0\times 10^{-5}}$

$\Rightarrow h=\frac{400}{2g}=20m$