Civil Engineering Fluid Mechanics Quiz

A mathematical equation representing a polynomial with five terms and different powers of the variable x. The equation has one real root in the range of 0 to 1.

A structural element designed to withstand tension forces, typically found in the lower part of a beam.

A structural element designed to withstand compression forces, typically located in the upper part of a beam.

A concrete section that is designed with sufficient reinforcement to carry the full load without failing in tension.

A concrete section where the amount of reinforcement is insufficient to carry the full load, resulting in failure in the tension zone.

Elements that strengthen steel by increasing its hardness and tensile strength.

An element that weakens steel by reducing its ductility and strength, making it brittle and prone to failure.

The ratio of Earth-Sun distance to Earth-Moon distance during a half-moon phase, approximately 382.

The curl of the gradient of a scalar field is always a null vector. This is a fundamental property of vector calculus, and it's a consequence of the fact that the gradient of a scalar field is irrotational.

The divergence of the curl of any vector field is always zero. This is another important result in vector calculus, and it's related to the fact that the curl of a vector field represents the rotation or vorticity of the field.

A Mohr's circle is a graphical representation of the state of stress at a point in a material. It's used to visualize the principal stresses and shear stresses acting on the material.

In the given example, we need to match the plane stress states (P, Q, R, S) with their corresponding Mohr's circles (I, II, III, IV) based on the stress values given.

A plane stress state is a condition where the stress components in one direction are negligible compared to the other two directions. This is a common assumption in many engineering problems, especially in thin plates or shells. The stress state is represented by the values of the normal stresses and shear stresses acting on the plane.

A uniformly distributed load is a load that acts over a continuous length of a beam and is spread evenly across that length. The load is represented by an intensity 'q' (force per unit length).

A beam is a structural element that is designed to resist loads that are primarily applied perpendicular to its longitudinal axis. Beams are commonly used in buildings, bridges, and other structures.

The support A is a fixed support, which means that it restricts both the translation and rotation of the beam at that point. The support B is a roller support, which means that it allows the beam to rotate but restricts its translation in one direction only.

The load intensity 'q' is applied to the beam between supports A and B, which means that the load is distributed only over that portion of the beam and not beyond.

The sum of the moments of all external forces acting on a rigid body about a given point is equal to the moment of inertia of the body about that point multiplied by the angular acceleration of the body.

The force acting on an object is directly proportional to the mass of the object and the acceleration of the object.

The ratio of the lengths L1/L2 is 2.00. This is because the torsional moment at each support is equal to the product of the polar moment of inertia and the angular displacement of the shaft at that point.

The inclination of failure planes with respect to the major principal plane for Rankine's active and passive earth pressure conditions is 30° and 60°, respectively. This can be understood with the help of Coulomb's theory of earth pressure, which describes the behaviour of soil under different stress conditions.

The velocity field is not irrotational, which means the fluid particles experience rotation. This can be determined by calculating the curl of the velocity field.

The total force acting on a surface due to the pressure of a fluid is calculated by integrating the pressure over the surface area. This force is perpendicular to the surface and is dependent on the depth of the fluid.

Activated carbon is used to remove pollutants from wastewater by adsorption - a process where pollutants bind to the activated carbon's surface. This is modeled by first-order kinetics, indicating the rate of removal is proportional to the concentration of the pollutant.

The time required for removing a pollutant by a specific percentage is calculated using the first-order reaction rate constant, which is a measure of how fast the reaction proceeds. The half-life of the reaction, the time taken for the pollutant concentration to reduce by half, is related to this constant.

To maintain the desired alkalinity in water treatment, we need to neutralize any alkalinity decrease caused by coagulation using quicklime. Quicklime reacts with water to create calcium hydroxide, which neutralizes bicarbonate ions and adjusts alkalinity.

Calcium bicarbonate, a compound naturally present in water, is required during coagulation. It is usually added as a pre-treatment step in water treatment.

The amount of quicklime (CaO) needed is linked to the amount of calcium bicarbonate (Ca(HCO3)2) consumed during coagulation. The chemical reaction between quicklime and calcium bicarbonate determines the necessary amount of quicklime.

The measure of the transverse slope of the track, expressed in millimeters, required to counteract the centrifugal force acting on a train navigating a curved track.

The average speed of all vehicles within a defined time and distance range.

The projected number of equivalent standard axles (msa) that will be applied to a pavement over its design life, considering vehicle growth and damage factors.

A type of support that allows a beam to rotate but restricts its movement in one direction.

A curved track with a radius of 437 meters.

The center-to-center distance between the rails of a train track.

A dimensionless parameter used to quantify the relationship between pore water pressure and effective stress changes in a soil during consolidation or shearing.

A type of triaxial test where the soil sample is consolidated under a given pressure (cell pressure) and then drained to remove excess pore water before applying axial stress. The test is then conducted under undrained conditions.

A graphical representation of the runoff response of a watershed to a specific rainfall event, typically a 1-hour unit of rainfall. It shows the discharge over time.

A method to derive a hydrograph for a longer duration (e.g., 3-hour UH) by combining and adjusting the ordinates of a shorter duration hydrograph (e.g., 1-hour UH).

The depth of flow in an open channel that corresponds to a specific discharge under steady-state conditions, where the weight of the flowing water is balanced by the frictional forces along the channel.

A hydraulic jump is a sudden transition from supercritical flow to subcritical flow in an open channel. It occurs when a high-velocity flow encounters a change in depth or geometry. The tail water depth is the upstream depth required to cause a hydraulic jump.

A measure of the flow rate per unit width of a channel or spillway. It represents the volumetric flow rate divided by the width of the flow.

A sudden transition from supercritical flow (high velocity, low depth) to subcritical flow (low velocity, high depth) in an open channel. It occurs due to energy dissipation and is characterized by a strong turbulent flow.