IN a streamine flow

Options

A. the speed of a particle always remains same
B. the velocity of a particle always remains same
C. the kinetic energies of all the particles arriving at a given point are the same
D. the momenta of all the particles arriving at a given point are the same

Answer

To solve the question regarding streamline flow, we need to analyze the characteristics of fluid motion in a streamline flow. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Streamline Flow
In a streamline flow, the fluid particles move along well-defined paths called streamlines. The key characteristics of streamline flow include that the particles do not intersect or collide with each other.

**Hint:** Remember that in streamline flow, each particle follows a smooth path without crossing others.

### Step 2: Analyze Particle Speed and Velocity
In a streamline flow, the speed of the particles can change depending on the cross-sectional area of the flow. According to the principle of continuity (A1V1 = A2V2), if the area of the flow changes, the velocity of the fluid particles must also change to conserve mass.

**Hint:** Consider how the flow area affects the velocity of the particles.

### Step 3: Kinetic Energy of Particles
Using Bernoulli's equation, we know that the total mechanical energy along a streamline is constant. The kinetic energy (KE) of the particles at a point is given by KE = (1/2)ρV². Since the flow is steady and the energy is conserved, the kinetic energy of the particles arriving at a point remains the same.

**Hint:** Recall the relationship between kinetic energy and velocity in the context of Bernoulli's principle.

### Step 4: Momentum of Particles
Since the particles do not collide and are all moving along the same streamline, the momentum of all particles at a point is also the same. Momentum is given by p = mv, where m is mass and v is velocity. In a steady flow, if the kinetic energy is constant, the momentum will also be constant.

**Hint:** Think about how mass and velocity contribute to momentum in a steady flow.

### Conclusion
From the analysis:
- The speed of the particles can change (not constant).
- The velocity of the particles can change (not constant).
- The kinetic energy of all particles arriving at a point is the same (constant).
- The momentum of all particles at a point is the same (constant).

Thus, the correct statements regarding streamline flow are that the kinetic energy and momentum of all particles at a point are the same.

**Final Answer:** The kinetic energy of all particles arriving at a point is the same, and the momentum of all particles at a point is the same.