The pressure drop in a pipe is directly proportional to the length of the pipe, as the fluid experiences friction along the pipe walls.

The velocity of a fluid in a pipe is inversely proportional to the diameter of the pipe, as the flow area increases with increasing diameter.

The flow rate in a pipe is directly proportional to the diameter of the pipe, as the flow area increases with increasing diameter.

The viscosity of a fluid affects the pressure drop, velocity, and flow rate in a pipe. Higher viscosity leads to higher pressure drop, lower velocity, and lower flow rate.

The Darcy-Weisbach equation is a general equation that relates pressure drop, velocity, and flow rate in a pipe, taking into account both laminar and turbulent flow conditions.

In laminar flow, the velocity profile in a pipe is parabolic, with the highest velocity at the center of the pipe and decreasing towards the pipe walls.

In turbulent flow, the velocity profile in a pipe is triangular, with the highest velocity near the center of the pipe and decreasing towards the pipe walls.

The Reynolds number is a dimensionless quantity used to determine the flow regime (laminar or turbulent) in a pipe.

The Moody diagram is a graphical representation of the relationship between pressure drop and Reynolds number in a pipe.

The friction factor in the Darcy-Weisbach equation is a function of both Reynolds number and relative roughness of the pipe.

The head loss in a pipe due to sudden expansion is always greater than the head loss due to sudden contraction.

The head loss in a pipe due to a bend is always greater than the head loss due to a straight pipe of the same length.

The head loss in a pipe due to a valve is always greater than the head loss due to a straight pipe of the same length.

The head loss in a pipe due to a pump is always less than the head loss due to a straight pipe of the same length.

The head loss in a pipe due to a turbine is always greater than the head loss due to a straight pipe of the same length.