Solution of Laplacian equation in three dimensions $$\frac{{{{\text{d}}^2}\varphi }}{{{\text{d}}{{\text{x}}^2}}} + \frac{{{{\text{d}}^2}\varphi }}{{{\text{d}}{{\text{y}}^2}}} + \frac{{{{\text{d}}^2}\varphi }}{{{\text{d}}{{\text{z}}^2}}} = 0$$ of water in a syphon, is done by A. Analytical method B. Khosla’s method C. Method of relaxation D. Unwin’s method

The correct answer is: C. Method of relaxation.

The method of relaxation is a numerical method for solving partial differential equations. It is based on the idea of iteratively updating the solution until it converges to the desired solution. The method of relaxation is particularly well-suited for solving elliptic partial differential equations, such as the Laplacian equation.

The Laplacian equation is a second-order partial differential equation that describes the equilibrium of a physical system. In the case of water in a syphon, the Laplacian equation can be used to describe the equilibrium of the water pressure. The method of relaxation can be used to solve the Laplacian equation and find the equilibrium pressure distribution in the syphon.

The method of relaxation is a relatively simple and efficient method for solving partial differential equations. It is often used in engineering and physics applications.

The other options are incorrect because they are not methods for solving partial differential equations.

• Analytical method is a method for solving problems by using mathematical equations. It is not a method for solving partial differential equations.
• Khosla’s method is a method for solving problems in structural engineering. It is not a method for solving partial differential equations.
• Unwin’s method is a method for solving problems in fluid dynamics. It is not a method for solving partial differential equations.