Khosla's theory of independent variables is used in the design of
a. Weirs and barrages
b. Cross regulators and head regulators
c. Modules

Explanation:

• Khosla’s Theory of Independent Variables is primarily applied in the design of subsurface flow structures to determine uplift pressures, exit gradients, and seepage paths below hydraulic structures.
• Khosla's theory is extensively used in the design of weirs and barrages to evaluate seepage forces and ensure safety against piping and uplift.
• Cross regulators and head regulators involve subsurface flow and potential uplift pressures, especially when located on permeable soils. Khosla’s theory is applied to design their foundations safely.
• Modules are outlet structures used for water distribution in irrigation, and their design does not require Khosla’s theory. They are more concerned with flow control rather than seepage analysis.

 Additional Information

• Khosla’s Theory of Independent Variables is an advancement over Bligh’s Creep Theory, developed for the design of subsurface flow under hydraulic structures.
• It accounts for pressure distribution and exit gradients more accurately in pervious soils using mathematical solutions from potential theory. 

Weirs and Barrages:

• These are major hydraulic structures built across rivers to divert or control flow.

• When built on permeable foundations, seepage beneath the structure poses a risk of piping and uplift pressure.

• Khosla’s theory helps determine:

  • Uplift pressures at various key points

  • Exit gradients at downstream end

  • Safe thickness of floor and cutoff depths

Head Regulators and Cross Regulators:

• Found in canal systems to regulate flow between main canals and branches.

• Subsurface flow analysis using Khosla’s theory ensures structural safety against uplift and seepage where these structures are located on sandy or alluvial foundations.

Modules:

• These are flow measuring and regulating devices (like outlets).

• Their function is hydraulic in nature, not structural against seepage.

• Hence, they do not require analysis using Khosla’s theory.