Properties of Fluids · Fluid Mechanics and Hydraulic Machines · GATE CE

The following figure shows a plot between shear stress and velocity gradient for materials/fluids P, Q, R, S, and T.

Which one of the following options is CORRECT?

A 2 m wide rectangular channel is carrying a discharge of 30 m³/s at a bed slope of 1 in 300. Assuming the energy correction factor as 1.1 and acceleration due to gravity as 10 m/s², the critical depth of flow (in meters) is __________ (rounded off to 2 decimal places).

The number of degrees of freedom for a natural open channel flow with a mobile bed is

A 30 cm diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m with hydraulic conductivity of 10 m/day. Under the steady pumping rate for a long time, the drawdowns in two observation wells located at 10 m and 100 m from the pumping well are 5 m and 1 m, respectively. The corresponding pumping rate (in m³/day) from the well is _____________ (rounded off to 2 decimal places).

The dimension of dynamic viscosity is :

A round-bottom triangular lined canal is to be laid at a slope of 1 in 1500, to carry a discharge of 25 m³/s. The side slopes of the canal cross-section are to be kept at 1.25H : 1V. If Manning’s roughness coefficient is 0.013, the flow depth (in meters) will be in the range of

A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: 1.50), silica sand (specific gravity: 2.60), and ilmenite sand (specific gravity: 4.20), is to be designed for treating water/wastewater. After backwashing, the particles should settle forming three layers: coarse anthracite particles at the top of the bed, silica sand in the middle, and small ilmenite sand particles at the bottom of the bed.

Assume

(i) Slow discrete settling (Stoke’s law is applicable)

(ii) All particles are spherical

(iii) Diameter of silica sand particles is 0.20 mm

The CORRECT option fulfilling the diameter requirements for this filter media is

A 500 m long water distribution pipeline P with diameter 1.0 m, is used to convey 0.1 m³/s of flow. A new pipeline Q, with the same length and flow rate, is to replace P. The friction factors for P and Q are 0.04 and 0.01, respectively. The diameter of the pipeline Q (in meters) is ______________ (rounded off to 2 decimal places).

A flow velocity field $\vec{V} : \vec{V}(x, y)$ for a fluid is represented by

$\vec{V} = 3 \hat{i} + (5x) \hat{j}$

In the context of the fluid and the flow, which one of the following statements is CORRECT?

A standard round bottom triangular canal section as shown in the figure has a bed slope of 1 in 200. Consider the Chezy’s coefficient as 150 m^1/2/s.


The normal depth of flow, y (in meters) for carrying a discharge of 20 m³/s is ___________ (rounded off to 2 decimal places).