Fluid Mechanics And Hydraulics

Explanation
The displacement thickness of a boundary layer refers to the distance by which the main flow is to be shifted from the boundary in order to maintain the continuity equation. This means that in order to account for the boundary layer, the main flow needs to be shifted by a certain distance to ensure that the mass flow rate remains constant. This displacement thickness is necessary to accurately analyze and calculate the flow properties within the boundary layer region.

Explanation
The correct relationship among displacement thickness (d), momentum thickness (m), and energy thickness (e) is that the energy thickness (e) is greater than the displacement thickness (d), and the displacement thickness (d) is greater than the momentum thickness (m). This means that the energy thickness represents the largest contribution to the total boundary layer thickness, followed by the displacement thickness, and finally the momentum thickness.

Explanation
The drag force experienced by an object is influenced by the projected area of the body, which is the cross-sectional area of the object as seen by the fluid flow. It is also dependent on the mass density of the fluid, as denser fluids tend to exert more resistance. Additionally, the velocity of the body plays a role in determining the drag force, as higher velocities result in greater resistance. Therefore, the correct answer is A, B, and C.

Explanation
Viscous force is the most important force in the motion of submarines underwater because water is a viscous fluid. Viscous force is the resistance offered by the fluid to the motion of an object through it. In the case of submarines, the shape and design of the submarine are crucial in order to minimize the drag caused by viscous forces. By reducing the drag, the submarine can move more efficiently through the water, allowing for better control and maneuverability. Therefore, understanding and managing viscous forces is essential for the effective operation of submarines underwater.

Explanation
A spillway model constructed to a scale of 1:4 gives a discharge of 5 m3/s. Since the scale of the model is 1:4, it means that every 1 unit in the model represents 4 units in the prototype. Therefore, to find the discharge from the prototype, we need to multiply the discharge from the model by the scale factor (4). 5 m3/s multiplied by 4 equals 20 m3/s. Therefore, the correct answer is 20 m3/s.

Explanation
In a river model, the length scale ratio is 1/100 and the depth scale ratio is 1/16. This means that every unit of length in the model represents 100 units of length in the actual river, and every unit of depth in the model represents 16 units of depth in the actual river.

To determine the discharge in the model, we need to consider the ratio of the cross-sectional areas of the model and the actual river. Since the length scale ratio is 1/100 and the depth scale ratio is 1/16, the area scale ratio is (1/100) * (1/16) = 1/1600.

Given that the peak discharge in the actual river is 25,600 m3/s, the discharge in the model can be calculated by multiplying the peak discharge by the area scale ratio: 25,600 * (1/1600) = 16 cumec.

Therefore, the correct answer is 4 cumec.