Answer:



When a valve is suddenly closed in a water main, a pressure wave propagates through the water. This pressure wave can cause the water to surge and can lead to damaging effects on the pipeline and surrounding structures.



The velocity of a pressure wave in water is determined by the bulk modulus and density of the water. For water, the bulk modulus is approximately 2.2 GPa and the density is approximately 1000 kg/m3. Therefore, the velocity of a pressure wave in water is given by:

v = sqrt(K/ρ)

where v is the velocity of the pressure wave, K is the bulk modulus, and ρ is the density of the water.

Substituting the values for water, we get:

v = sqrt(2.2 x 109 / 1000) = 1483 m/s



When a valve is suddenly closed, the water in the pipeline will continue to flow due to its inertia. This inertia generates a pressure head, known as the inertia head, which opposes the pressure wave and can cause the water to surge.

The inertia head is given by:

H = (v^2 / 2g)

where H is the inertia head, v is the velocity of the water, and g is the acceleration due to gravity (9.81 m/s2).

Substituting the values, we get:

H = (1^2 / 2 x 9.81) = 0.051 m

Therefore, the inertia head at the valve will be approximately 0.051 m. This value represents the height to which the water will surge due to the inertia of the water in the pipeline.

100m