Introduction:
In this problem, we are given two reservoirs with different water levels that are connected by two pipes A and B in parallel. We are also given that the diameter of pipe A is twice that of pipe B. We need to find the ratio of frictional loss in pipe B to that of pipe A.

Understanding the Problem:
To solve this problem, we need to understand the concept of frictional loss in pipes. Frictional loss occurs due to the resistance offered by the pipe walls to the flow of water. It depends on various factors such as the diameter of the pipe, the length of the pipe, the roughness of the pipe walls, and the velocity of the flow.

Solution:
To find the ratio of frictional loss in pipe B to that of pipe A, we can use the Darcy-Weisbach equation, which relates the frictional loss to the pipe diameter, length, roughness, and velocity of flow.

Darcy-Weisbach Equation:
The Darcy-Weisbach equation for calculating the frictional loss in a pipe is given by:

h = (f * L * V^2) / (2 * g * D)

Where:
h = frictional loss (head loss)
f = friction factor
L = length of the pipe
V = velocity of flow
g = acceleration due to gravity
D = diameter of the pipe

Applying the Equation:
Let's assume that the water flows through both pipes at the same velocity and the length and roughness of the pipes are the same. Since the diameter of pipe A is twice that of pipe B, we can denote the diameter of pipe B as 'd' and the diameter of pipe A as '2d'.

Using the Darcy-Weisbach equation for pipe A, we have:
hA = (fA * L * V^2) / (2 * g * 2d)

Using the Darcy-Weisbach equation for pipe B, we have:
hB = (fB * L * V^2) / (2 * g * d)

Ratio of Frictional Loss:
To find the ratio of frictional loss in pipe B to that of pipe A, we can divide the equation for pipe B by the equation for pipe A:

hB / hA = (fB * L * V^2) / (2 * g * d) / (fA * L * V^2) / (2 * g * 2d)

Simplifying the equation, we get:
hB / hA = fB / fA

Therefore, the ratio of frictional loss in pipe B to that of pipe A is equal to the ratio of their friction factors.

Conclusion:
In conclusion, the ratio of frictional loss in pipe B to that of pipe A is equal to the ratio of their friction factors. The friction factor depends on various factors such as the diameter of the pipe, the roughness of the pipe walls, and the velocity of the flow.