List of top Water Resources Engineering Questions asked in GATE CE

A 2m × 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentration 5 g/m3 at the rate of 2 litre/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modelled using the following differential equation:
\(\frac {dm}{dt}+\frac {m}{6000+t}=0.01\)
where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is _____ (rounded off to 2 decimal places).
A 5m × 5m closed tank of 10 m height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use \(γ_w=10\ kN/m^3\) and Specific gravity of oil = 0.8
water reservoir
The total force (in kN) due to pressure on the side PQR of the tank is _____ (rounded off to the nearest integer).
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 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)
A 2 m × 1.5 m tank of 6 m height is provided with a 100 mm diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to 5 m height. Consider the average value of discharge coefficient as 0.6 and acceleration due to gravity (g) as 10 m/s2. After unplugging the orifice, the time (in seconds) taken for the water level to drop from 5 m to 3.5 m under free discharge condition is _________ (rounded off to 2 decimal places).
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 homogeneous earth dam has a maximum water head difference of 15 m between the upstream and downstream sides. A flownet was drawn with the number of potential drops as 10 and the average length of the element as 3 m. Specific gravity of the soil is 2.65. For a factor of safety of 2.0 against piping failure, void ratio of the soil is ________ (rounded off to 2 decimal places).
Consider the statements P, Q, and R.
P : Compacted fine-grained soils with flocculated structure have isotropic permeability.
Q : Phreatic surface/line is the line along which the pore water pressure is always maximum.
R : The piping phenomenon occurring below the dam foundation is typically known as blowout piping.
Which of the following option(s) is/are CORRECT ?
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 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).
A spillway has unit discharge of 7.5 m3/s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is_____ (rounded off to 2 decimal places).
The ordinates of a 1-hour unit hydrograph (UH) are given below.
Time (hours)01234567891011
Ordinates of 1-hour UH (m3/s)013508095855535151030
These ordinates are used to derive a 3-hour UH. The peak discharge (in m3/s) for the derived 3-hour UH is _____ (rounded off to the nearest integer).
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 m1/2/s.
A standard round bottom triangular canal section
The normal depth of flow, y (in meters) for carrying a discharge of 20 m3/s 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?
For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission standard (based on 11% Oxygen) for HCl is 50 mg/Nm3 and the measured concentrations of HCl and Oxygen in flue gas are 42 mg/Nm3 and 13%, respectively.
Assuming 21% Oxygen in air, the CORRECT statement is:
Is this incompressible or irrotational?
\(V = 3î + 5 xĴ\)