The direction of water flow is from point A to point B, as the upstream pressure at A is higher than downstream pressure at B despite B being at a higher elevation. The head loss due to friction is calculated using Bernoulli's equation which incorporates the pressure difference, gravity, and elevation difference between points A and B.
This physics problem involves the principles of fluid dynamics and Bernoulli's equation to determine the direction of flow and the head lost due to friction in the water supply line. First, we'll use Bernoulli's equation to find out the direction in which the water is flowing by comparing the pressures at points A and B, taking into account the elevation difference and the given flow rate. Then, we'll calculate the head lost due to friction.
To find the direction of the flow, we need to consider the elevation head and the pressure head. Given that B is higher than A by 3 meters, and the pressure at A is greater than at B, we can deduce that water flows from A to B against the gravity, which means A is the higher pressure point upstream and B is downstream.
To calculate the head lost in friction (also known as head loss), we'll use Bernoulli's equation modified for head loss, which is expressed as:
HL = (PA - PB)/(ρg) + zA - zB
Where HL is the head loss, PA and PB are pressures at points A and B, ρ is the density of water, g is the acceleration due to gravity, and zA and zB are the elevations of points A and B, respectively. By plugging in the given pressures and elevations, we can find out the head loss in the pipe due to friction.