Flow nets in civil engineering

Introduction
Flow nets are graphical representations of fluid flow through porous media. They are commonly used in civil engineering to analyze seepage through dams, slopes, foundations, and other geotechnical structures. Flow nets consist of a series of flowlines and equipotential lines that provide information about the flow direction, velocity, and pressure distribution.

Correct statements about flow nets
The correct statements about flow nets are:

b) For non-isometric mediums, flow fields are rectangular
In flow nets, the flow fields are generally rectangular for non-isometric mediums. This means that the flowlines and equipotential lines intersect at right angles. This relationship is based on the assumption that the medium is homogeneous and isotropic. However, in reality, the flow fields may deviate from perfect rectangles due to the presence of irregularities or heterogeneities in the medium.

c) The velocity of flow is perpendicular to equipotential lines
The velocity of flow in a flow net is always perpendicular to the equipotential lines. This is due to the fact that flow occurs along the direction of steepest hydraulic gradient, which is perpendicular to the equipotential lines. The equipotential lines represent lines of equal hydraulic head, and the flow moves from higher hydraulic head to lower hydraulic head.

d) Laplace equation is valid in flow nets
The Laplace equation, also known as the Laplace's equation for potential flow, is valid in flow nets. The Laplace equation states that the sum of the second partial derivatives of the flow function with respect to the coordinates is equal to zero. In other words, it describes the conservation of mass in potential flow. Flow nets satisfy the Laplace equation, which allows engineers to solve for the flow velocity and pressure distribution using mathematical techniques such as the method of images or conformal mapping.

Incorrect statement about flow nets
The incorrect statement is:

a) Flow always exists on flowlines only
Flow does not exist only on flowlines in flow nets. Flow occurs both along the flowlines and perpendicular to the equipotential lines. The flowlines represent the path of flow, while the equipotential lines represent lines of equal hydraulic head. The flow moves from higher hydraulic head to lower hydraulic head, and this movement occurs both along the flowlines and perpendicular to the equipotential lines.

Conclusion
Flow nets are useful tools in civil engineering for analyzing seepage and fluid flow through porous media. They provide valuable information about flow direction, velocity, and pressure distribution. The correct statements about flow nets are that for non-isometric mediums, flow fields are rectangular, the velocity of flow is perpendicular to equipotential lines, and the Laplace equation is valid in flow nets.