The equation of continuity holds good when the flow is steady, one dimensional, and velocity is uniform at all the cross sections.
A steady flow is a flow in which the velocity of the fluid at any point in the flow does not change with time. A one-dimensional flow is a flow in which the velocity of the fluid is constant in all directions except one. A uniform flow is a flow in which the velocity of the fluid is the same at all points in the flow.
The equation of continuity states that the mass of fluid flowing through a given cross section of a pipe in a given time is constant. This means that the product of the area of the cross section and the velocity of the fluid at that cross section is constant.
The
equation of continuity can be derived from the principle of conservation of mass. The principle of conservation of mass states that mass can neither be created nor destroyed. This means that the total mass of fluid flowing into a system must equal the total mass of fluid flowing out of the system.The equation of continuity is a useful tool for analyzing fluid flow. It can be used to calculate the velocity of the fluid at any point in
the flow, the area of the cross section of a pipe, and the mass of fluid flowing through a pipe.