Question

The mean flow velocity of water in an open channel having an average depth of 0.2 m, and with Froude Number 4, is ________ m/s. (Round off to one decimal place) (Use $g = 9.8 ms^{-2}$)

Answer 1

Correct Answer: 5.6

Calculating the Mean Flow Velocity using the Froude Number

Step 1: Understanding the Formula

The Froude Number (Fr) is given by the equation: 

\[ Fr = \frac{V}{\sqrt{g \cdot D}} \]

Where:

• V is the mean flow velocity in m/s.
• g is the acceleration due to gravity (9.8 m/s²).
• D is the depth of the flow (0.2 m).

Step 2: Rearranging the Equation to Solve for V

Rearranging the equation to solve for the mean flow velocity (V):

\[ V = Fr \cdot \sqrt{g \cdot D} \]

Step 3: Substituting the Given Values

Substituting the given values into the equation:

\[ V = 4 \cdot \sqrt{9.8 \cdot 0.2} \]

First, calculate \( g \cdot D = 9.8 \cdot 0.2 = 1.96 \).

Now, take the square root:

\[ \sqrt{1.96} = 1.4 \]

Thus, the mean flow velocity (V) is:

\[ V = 4 \cdot 1.4 = 5.6 \, \text{m/s} \]

Final Answer:

The mean flow velocity is: 5.6 m/s (rounded to one decimal place).