Q1: For solving network problems of pipes, necessary condition is

ANS:D - all the above.

1. Continuity Equation: The continuity equation states that the mass flow rate of an incompressible fluid within a closed system remains constant. It is based on the principle of conservation of mass and is expressed mathematically as �=�⋅�Q=A⋅v, where �Q is the volumetric flow rate, �A is the cross-sectional area of the pipe, and �v is the velocity of the fluid.
2. Energy Equation: The energy equation, also known as the Bernoulli equation, is used to analyze fluid flow along a streamline and describes the conservation of energy in a fluid flow system. It takes into account changes in pressure, velocity, and elevation along the flow path. The energy equation is crucial for determining the pressure head, velocity head, and elevation head of the fluid at different points within the system.
3. Darcy-Weisbach Equation: The Darcy-Weisbach equation is an empirical formula used to calculate the pressure drop or head loss due to friction in a pipe system. It relates the head loss to the flow rate, pipe diameter, length of the pipe, and the friction factor. The Darcy-Weisbach equation is widely used in hydraulic engineering and fluid mechanics for analyzing pipe networks and determining the required pipe sizes for given flow conditions.