September 4, 2008


Filed under: Uncategorized — Rajnikant Khatsuria @ 10:06 pm


(For similar topics refer https://hydrotopics.wordpress.com)


(email: rmkhatsuria@rediffmail.com)


Although, one differentiates between a fluid and a rigid body, there are many similarities in the fluid dynamics and the dynamics of rigid body. Both are covered under the general theory of continuum mechanics. Several problems concerning flow of water have been successfully treated with the principles of rigid body dynamics. As an example, the equations of the trajectory of a high velocity jet of water issuing from a nozzle have been derived on the basis of dynamics of rigid body, assuming that the flow of water consists of a series of water particles travelling in succession, at a given velocity and inclination. It could also account for the effects of external force such as resistance by air. We know that the flow of water is more susceptible to this force than a rigid body, and the analysis is applicable here also.  However, beyond this limit, the treatment differs. The flow of water is subjected to an internal force also, conspicuously absent in a rigid body. This is the internal turbulence in the flow that works to exert a retarding effect. If the velocity is beyond certain limit, the flow also entrains air from the surroundings and then it is known as two-phase flow. Entrainment of air in the flow of water may result in bulking and disintegration of the water mass. These phenomena have, of course been analyzed- only a little theoretically and mostly empirically. Thus, the flow of water alone is amenable to the analysis, much the way as in the dynamics of rigid body, but the flow of mixture of water and air needs different treatment.

Another example of the two-phase flow is the mixture of water and sediment. If water flows along a bed consisting of loose material like sand, gravel or clay particles, this material can also be picked up by the flow and carried along with it. While, both the flow of clear water and rigid particles can be analyzed individually, a sediment laden flow requires different approach and here again, much is empirical.

So what are the implications of such accompanied flows, in addition to their not being amenable to analysis through simple mechanics? Entrainment of air in flow of water dampens part of turbulence and results in reduction of drag at the boundary of the flow.  Air entrainment results in bulking of water mass so the depth increases in comparison to clear water depth. This would necessitate higher side walls to contain the flow. Yet, air entrainment is not always a problem; it is a remedy also! It is known that a small quantity of air entrained in flow (some 8% or so) close to the flow boundary significantly reduces cavitation damage. The surfaces of spillways, outlets and tunnels subjected to flows of high velocity-of the order of 25m/s or so-are protected against cavitation damage by artificially entraining them with required quantity of air. This technique of forced aeration has been successfully applied to a large number of spillways, outlets and tunnels, to reduce cavitation risk, during the last two decades. The devices that force air in the bottom layers of flow are known as aerators.

While the air entrainment in the bottom layers of high velocity flows on spillway surfaces is beneficial in preventing cavitation damage, flows with higher air contents in bottom layers in stilling basins and river downstream are detrimental to aquatic biota. There is some conflict between the two objectives discussed above. More discussion on how these are tackled will be discussed later.

Sediment laden flows on surfaces of hydraulic structures are always a problem. Flows containing coarse sediment in bottom layers with high velocities have damaged surfaces of spillways, outlets and tunnels by abrasion. Even when special arrangements are made to evacuate sediment load from the flow, presence of finer material in suspension have damaged blades of hydro turbines by abrasion. Devices called settling tanks are employed to evacuate as much of the sediment as possible before the flow is admitted to power plant. If the flow containing coarse sediment is to pass down a spillway, the best course would be to provide a protective coating on the spillway surface. In some cases, a large part of sediment can be flushed out by a special operation.

          (Copyright: Neither this article nor any part may be reproduced, copied or transmitted in any form without permission in writing from the author)



         (In the next issue:  Remodeling of existing spillways)


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