The horse power transmitted through a pipe is maximum when the ratio of loss of head due to friction and total head supplied is A. $$\frac{1}{3}$$ B. $$\frac{1}{4}$$ C. $$\frac{1}{2}$$ D. $$\frac{2}{3}$$

The correct answer is $\boxed{\frac{1}{2}}$.

The head loss due to friction is given by the following equation:

$$h_f = \frac{L}{D} \cdot \frac{v^2}{2g}$$

where:

• $h_f$ is the head loss due to friction
• $L$ is the length of the pipe
• $D$ is the diameter of the pipe
• $v$ is the velocity of the fluid
• $g$ is the acceleration due to gravity

The total head supplied is given by the following equation:

$$h_t = h_f + h_g$$

where:

• $h_t$ is the total head supplied
• $h_f$ is the head loss due to friction
• $h_g$ is the head due to gravity

The horsepower transmitted through a pipe is given by the following equation:

$$P = \frac{Q \cdot h_t}{\eta}$$

where:

• $P$ is the horsepower transmitted through the pipe
• $Q$ is the flow rate
• $h_t$ is the total head supplied
• $\eta$ is the efficiency of the pump

The efficiency of a pump is typically between 0.7 and 0.9.

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