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For any channel section, the specific energy increases with
(i) increase in depth of sub-critical flow
(ii) increase in depth of super-critical flow
(iii) decrease in depth of sub-critical flow
(iv) decrease in depth of super-critical flow
The correct answer is
- a)(i) and (iv)
- b)(i) and (ii)
- c)(ii) and (iii)
- d)(iii) and (iv)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
For any channel section, the specific energy increases with(i) increa...
The specific energy of a channel is a measure of the energy per unit weight of a fluid in a channel. It is defined as the sum of the kinetic energy and the potential energy per unit weight of the fluid.
In subcritical flow, the specific energy of a channel increases with an increase in depth. This is because an increase in depth leads to an increase in the potential energy of the fluid, which in turn leads to an increase in the specific energy.
In supercritical flow, the specific energy of a channel decreases with an increase in depth. This is because an increase in depth leads to a decrease in the kinetic energy of the fluid, which in turn leads to a decrease in the specific energy.
Therefore, the correct answer is option (a) (i) and (iv).
Most Upvoted Answer
For any channel section, the specific energy increases with(i) increa...
Explanation:
The specific energy is defined as the energy per unit weight of flow. It is given by the expression:
E = (y + Q^2/2gA^2)
where, E is the specific energy, y is the depth of flow, Q is the discharge, g is the acceleration due to gravity, and A is the cross-sectional area of flow.
Now, let us consider the effect of various factors on the specific energy of a channel section:
(i) Increase in depth of sub-critical flow: When the depth of flow in a sub-critical channel section increases, the specific energy also increases. This is because the velocity of flow decreases with increase in depth, and hence the kinetic energy of flow decreases. However, the potential energy of flow increases due to the increase in depth, and this results in an overall increase in specific energy.
(ii) Increase in depth of super-critical flow: When the depth of flow in a super-critical channel section increases, the specific energy decreases. This is because the velocity of flow increases with increase in depth, and hence the kinetic energy of flow increases. However, the potential energy of flow decreases due to the decrease in specific weight of flow with increase in velocity, and this results in an overall decrease in specific energy.
(iii) Decrease in depth of sub-critical flow: When the depth of flow in a sub-critical channel section decreases, the specific energy also decreases. This is because the velocity of flow increases with decrease in depth, and hence the kinetic energy of flow increases. However, the potential energy of flow decreases due to the decrease in depth, and this results in an overall decrease in specific energy.
(iv) Decrease in depth of super-critical flow: When the depth of flow in a super-critical channel section decreases, the specific energy increases. This is because the velocity of flow decreases with decrease in depth, and hence the kinetic energy of flow decreases. However, the potential energy of flow increases due to the increase in specific weight of flow with decrease in velocity, and this results in an overall increase in specific energy.
Therefore, the correct answer is option 'A', i.e., (i) and (iv).
The specific energy is defined as the energy per unit weight of flow. It is given by the expression:
E = (y + Q^2/2gA^2)
where, E is the specific energy, y is the depth of flow, Q is the discharge, g is the acceleration due to gravity, and A is the cross-sectional area of flow.
Now, let us consider the effect of various factors on the specific energy of a channel section:
(i) Increase in depth of sub-critical flow: When the depth of flow in a sub-critical channel section increases, the specific energy also increases. This is because the velocity of flow decreases with increase in depth, and hence the kinetic energy of flow decreases. However, the potential energy of flow increases due to the increase in depth, and this results in an overall increase in specific energy.
(ii) Increase in depth of super-critical flow: When the depth of flow in a super-critical channel section increases, the specific energy decreases. This is because the velocity of flow increases with increase in depth, and hence the kinetic energy of flow increases. However, the potential energy of flow decreases due to the decrease in specific weight of flow with increase in velocity, and this results in an overall decrease in specific energy.
(iii) Decrease in depth of sub-critical flow: When the depth of flow in a sub-critical channel section decreases, the specific energy also decreases. This is because the velocity of flow increases with decrease in depth, and hence the kinetic energy of flow increases. However, the potential energy of flow decreases due to the decrease in depth, and this results in an overall decrease in specific energy.
(iv) Decrease in depth of super-critical flow: When the depth of flow in a super-critical channel section decreases, the specific energy increases. This is because the velocity of flow decreases with decrease in depth, and hence the kinetic energy of flow decreases. However, the potential energy of flow increases due to the increase in specific weight of flow with decrease in velocity, and this results in an overall increase in specific energy.
Therefore, the correct answer is option 'A', i.e., (i) and (iv).
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