For a sharp-crested weir with crest level Ps above the base and head of water H

Question

For a sharp-crested weir with crest level Ps above the base and head of water H above the crest level, the Bernoulli equation can be applied along a streamline between sections 1 and 2 Energy Line dh 2 2? Side View Front View Fig 3.1 Flow over a weir y 2g y 2g where p= pressure at location z, V is the velocity at location z and ? is the weight density (spg) of water Energy losses between sections 1 and 2 are assumed to be negligible. Velocity V1 is assumed to be uniform across section 1 (i.e. the streamlines at section 1 are straight, parallel and evenly spaced). At section 2, velocity V2 varies depending on the elevation of point B. At section 2 the water is a jet in the atmosphere and consequently the total head consists of elevation plus velocity heads. Therefore (3.2) 2g where Ps is the height of the base of the V-notch. Hence,

Explanation / Answer

Bernoullis equation is applied at sections 1 and 2. Section 1 is very large compared to the constricted section 2 of the notch. We know that if cross sectional area is large then velocity becomes low. That is why we can neglect the velocity at section 1. Hence the approach velocity head is neglected.

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