**Explanation:**

The average velocity in a vertical stream, denoted as *Vin*, is related to the surface velocity of the stream, denoted as *Vs*. According to the given question, we need to determine the relationship between *Vin* and *Vs*.

One of the fundamental principles of fluid mechanics is the principle of continuity, which states that the mass flow rate of a fluid is constant in a steady flow. This principle can be applied to the stream to relate the velocities at different points.

The mass flow rate, denoted as *Q*, is given by the equation:

*Q = ρAv*

Where:
- *Q* is the mass flow rate
- *ρ* is the density of the fluid
- *A* is the cross-sectional area of the stream
- *v* is the velocity of the fluid

**Applying the principle of continuity:**

Let's consider two different cross-sections in the stream: the surface cross-section and a vertical cross-section.

At the surface cross-section, the mass flow rate can be expressed as:

*Qs = ρAs Vs*

At the vertical cross-section, the mass flow rate can be expressed as:

*Qin = ρAin Vin*

Since the principle of continuity states that the mass flow rate is constant, we can equate the two expressions:

*Qs = Qin*

Substituting the expressions for *Qs* and *Qin*:

*ρAs Vs = ρAin Vin*

**Simplifying the equation:**

We can simplify the equation by canceling out the density term and rearranging the equation:

*As Vs = Ain Vin*

The cross-sectional area at the surface (*As*) is typically larger than the cross-sectional area at the vertical (*Ain*) due to the spreading of the stream as it flows downstream. Therefore, we can assume that *As > Ain*.

Dividing both sides of the equation by *As*:

*Vs = (Ain/As) Vin*

Since *Ain/As < 1*="" (because="" *as="" /> Ain*), we can conclude that:

*Vs < />

Therefore, the average velocity in the vertical stream (*Vin*) will be greater than the surface velocity (*Vs*).

**Answer:**

The correct answer to the given question is option C: *0.9 Vs*. This is because the average velocity in the vertical stream (*Vin*) will be approximately 0.9 times the surface velocity (*Vs*).