This set of Irrigation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Seepage Theories – Khosla’s Theory”.
1. The laplacian equation represents two sets of curves intersecting orthogonally.
Explanation: The laplacian equation represents two sets of curves, namely one set of lines called streamlines and the other set called equipotential lines. These two sets of lines intersect orthogonally. The resultant flow diagram of these two sets is a flow net.
2. What is the path represented by the streamlines?
a) Hydraulic Jump
b) Flow Net
c) Energy Dissipation
d) Water Flow
Explanation: The streamlines represent a path along which the water flows through the subsoil. Every particle entering the upstream will trace its own path and represents its own streamline.
3. How many corrections are needed for the complex profile broken from simple forms, to be valid?
Explanation: The corrections needed are correction for mutual interference of piles, correction for thickness of floor, and correction for slope of the floor.
4. By how many considerations the depth downstream vertical cutoff is governed?
Explanation: In order to prevent undermining, it is absolutely necessary to provide a reasonably deep vertical cutoff at the downstream end of the downstream pucca floor. The depth of this downstream vertical cutoff is governed by two considerations, namely maximum depth of scour and safe exit gradient.
5. Khosla’s theory of flow nets says that the loss head does not take place uniformly.
Explanation: The flow nets proposed by the khosla’s theory says that the loss head depends upon the whole geometry of the figure, that is the shape of foundation, depth of impervious boundary and levels of upstream and downstream beds. If the equipotential lines are traced closer, then the loss of head is fast and vice versa.
6. What is laplacian equation?
a) d2φ / dx2 + d2Φ/dz2
b) d2Φ / dx2 + d2Φ/dz2
c) dΦ / dx + d2Φ/dy2
d) d2φ / dx2 + d2Φ/dz
Explanation: The laplacian equation is based on Φ(flow potential) which is a combination of flow potential Kh, where K is coefficient of permeability of soil and h is residual head at any point. The equation is represented as d2Φ/dx2 + d2Φ/dz2.
7. What type of points is needed to be joined to form an equipotential line?
a) Equal Pressure Points
b) Residual Heads which still need Energy Dissipation
c) Velocity Gradient Points
d) Points of intersection of Streamlines and Velocity Components
Explanation: Streamlines enter from the upstream with some head (H), but in case of equipotential lines it is considered that in downstream side water is not present. So, even though energy dissipation takes place there will some residual head (h) will be present at certain points on the streamlines. Therefore, joining these points together forms an equipotential line.
8. The component of which force is to be counterbalanced so that the soil grains remain stable?
a) Upthrust Pressure Forces
b) Forces due to Velocity Components
c) Pressure Force
d) Seepage Water Force
Explanation: The seepage water exerts a force tangential to the streamlines at each point in the direction of the flow. This force, when resolved has an upward component from point 5, where the streamline turns upward. So, therefore in order to keep the soil grains stable the upward component of this force should be counterbalanced by the submerged weight of the soil grain.
9. What is the name of the gradient pressure at the exit end?
a) Gradient of Pressure
b) Exit Gradient
c) Streamline Gradient
d) Equipotential Gradient
Explanation: The upward component of the seepage water force is the disturbing force, and it is proportional to the gradient pressure of water at that point. This gradient pressure of water at the exit end is termed as an exit gradient.
10. Which method is evolved by khosla for designing of hydraulic structures?
a) Method of Gradients
b) Method of Variables
c) Method of Independent Variables
d) Method of Flow Nets
Explanation: Generally in order to know the seepage below the hydraulic structures the flownet is used. In other words we must solve the laplacian equations by mathematical method, or electrical method, or graphical method with the help of streamlines and equipotential lines and some boundary conditions. But, this is a time taking process and solving is more complicated. So, therefore for the designing of hydraulic structures khosla introduced a easy, simple and accurate approach called a method of independent variables.
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