Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \,m^3 \,s^{-1}$. The velocity of water at a point where the radius of the pipe is $10 \,cm$ is (in $\,m/s$)

$A$ motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is increased to $P_1$. The ratio of $P_1$ to $P_0$ is

Assertion $(A):$ The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up but tends to narrow down when held vertically down.
Reason $(R):$ In any steady flow of an incompressible fluid,the volume flow rate of the fluid remains constant.

Water flows through a hose pipe whose internal diameter is $4 \,cm$ at a speed of $1 \,ms^{-1}$. If water has to emerge at a speed of $4 \,ms^{-1}$, then the diameter of the nozzle should be (in $\,cm$)

Explain steady flow.

What is steady flow?