NEB Class 12 Science Fluids Mechanics Question Paper 2082 (Set A) Nepal

Volume $= 1.5 \times 1 \times 2 = 3\,\text{m}^3$. If the apparent weight in water is $300\,\text{kgf}$, then $W - F_b = 300$, where $F_b = 1000 \times 3 = 3000\,\text{kgf}$. So $W = 3300\,\text{kgf}$, giving $G = 3300/3000 = 1.1$.

Constant rate (steady) but the velocity changes along the expanding tube (non-uniform): steady non-uniform flow.

In open channel flow, flow is laminar if Reynolds number is less than about 500 (often quoted 500–600).

The continuity equation expresses conservation of mass.

The difference between the energy gradient (hydraulic gradient) line and the total energy line is the velocity (kinetic) head.

In a venturimeter the divergent cone is kept longer than the convergent cone (to minimize losses).

A weir with end contractions has an effective width less than the width of the channel.

$Re = \frac{\rho v D}{\mu} = \frac{1000 \times 0.8 \times 0.05}{1.6\times10^{-2}} = 2500$. Since $2000 < Re < 4000$, the flow is in the transition range.

Types of flow on the basis of Reynolds number

The Reynolds number is $Re = \dfrac{\rho v D}{\mu}$ (for pipes) and it classifies flow as:

1. Laminar flow — fluid moves in smooth, parallel layers; viscous forces dominate. In pipe flow $Re < 2000$ (in open channels $Re < 500$).
2. Transitional flow — flow alternates between laminar and turbulent. Pipe: $2000 < Re < 4000$ (open channel: $500 < Re < 2000$).
3. Turbulent flow — irregular, mixing motion with eddies; inertial forces dominate. Pipe: $Re > 4000$ (open channel: $Re > 2000$).

Difference between supercritical and subcritical flow

These are classified using the Froude number $Fr = \dfrac{v}{\sqrt{gy}}$, where $y$ is the depth of flow.

When $Fr = 1$ the flow is critical.

Bernoulli's Theorem (Statement)

For a steady, incompressible, non-viscous flow, the total energy (pressure energy + kinetic energy + potential energy) per unit weight of a flowing fluid remains constant at every point along a streamline.

where $\dfrac{p}{\rho g}$ is the pressure head, $\dfrac{v^2}{2g}$ is the velocity (kinetic) head, and $z$ is the datum (potential) head.

Assumptions made

1. The fluid is ideal (non-viscous), so there is no loss of energy due to friction.
2. The fluid is incompressible (constant density).
3. The flow is steady.
4. The flow is along a streamline (irrotational).
5. No external energy is added or removed (no pump or turbine).

Engineering applications

1. Venturimeter — measurement of discharge/flow rate in pipes.
2. Orifice meter and nozzle meter — flow measurement.
3. Pitot tube — measurement of fluid velocity.
4. Flow over weirs and notches.
5. Working principle of aeroplane wing lift and carburettor/atomizer.