Motion of a liquid in a tube is describe by

Options

A. Bernoullis theorem
B. Poiseuille's equation
C. Stoke's law
D. Archimedes principle.

Answer

To solve the question regarding the motion of a liquid in a tube, we need to analyze the relevant principles and theorems that describe this phenomenon. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Theorems
We need to consider the various theorems that describe the motion of liquids in tubes. The relevant principles include:
1. Bernoulli's Theorem
2. Poiseuille's Equation
3. Archimedes' Principle
4. Stokes' Law

### Step 2: Understand Bernoulli's Theorem
Bernoulli's theorem states that in a flowing fluid, an increase in the fluid's speed occurs simultaneously with a decrease in pressure or potential energy. This theorem is particularly relevant for understanding the motion of liquids in tubes, as it relates pressure and velocity.

### Step 3: Analyze Poiseuille's Equation
Poiseuille's equation describes the volumetric flow rate of a viscous fluid through a cylindrical pipe. It is given by:
\[ Q = \frac{\pi P r^2}{8 \eta l} \]
where:
- \( Q \) is the volumetric flow rate,
- \( P \) is the pressure difference,
- \( r \) is the radius of the tube,
- \( \eta \) is the dynamic viscosity of the fluid,
- \( l \) is the length of the tube.

While this equation is important for understanding flow rates, it is more specific to viscous flow rather than general motion.

### Step 4: Consider Archimedes' Principle
Archimedes' principle explains the buoyant force acting on an object submerged in a fluid. While it is important in fluid mechanics, it does not specifically describe the motion of liquids in tubes.

### Step 5: Review Stokes' Law
Stokes' law describes the drag force acting on spherical objects moving through a viscous fluid. It is given by:
\[ F = 6 \pi \eta r v \]
This law is relevant for small particles in a fluid but does not describe the overall motion of liquids in tubes.

### Step 6: Conclusion
Among the theorems discussed, **Bernoulli's theorem** is the most accurate and relevant for describing the motion of a liquid in a tube, as it directly relates the pressure and velocity of the fluid in motion.

### Final Answer
The motion of a liquid in a tube is described by **Bernoulli's theorem**.

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