For a given discharge in an open channel, there are two depths which have the same specific energy. These two depths are known as
In a 5 m wide rectangular channel, the velocity $u$ distribution in the vertical direction $y$ is given by $ u=1.25y^\frac16 $ . The distance y is measured from the channel bed. If the flow depth is 2 m, the discharge per unit width of the channel is
A rough pipe of 0.5 m diameter, 300 m length and roughness height of 0.25 mm, carries water (kinematic viscosity $ 0.9\times10^{-6} $ m^{2}/s) with velocity of 3 m/s. Friction factor ($ f $) for laminar flow is given by $ f=64/R_e $, and for turbulent flow it is given by $ \frac1{\sqrt f}=2\;\log_{10}\left(\frac rk\right)+1.74 $, where, $ R_e $ = Reynolds number, r = radius of pipe, k = roughness height and $ g=9.81$ m/s^{2} . The head loss (in m, up to three decimal places) in the pipe due to friction is ______
A sluice gate used to control the flow in a horizontal channel of unit width is shown in the figure.
It is observed that the depth of flow is 1.0 m upstream of the gate , while the depth is 0.2 m downstream of the gate. Assuuming a smooth flow transition across the sluice gate, i.e, without any energy loss, and the acceleration due to gravity as 10 m/s^{2}, the discharge (in m^{3}/s, up to two decimal places) passing under the sluice gate is _______
If a centrifugal pump has an impeller speed of N (in rpm), discharge Q (in m^{3}/s) and the total head H (in m), the expression for the specific speed N_{s} of the pump is given by
A 1 m wide rectangular channel carries a discharge of 2 m^{3}/s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two deimal places) is equal to ____________
Water is pumped at a steady uniform flow rate of 0.01 m^{3}/s through a horizontal smooth circular pipe of 100 mm diameter. Given that the Reynolds number is 800 and g is 9.81 m/s^{2}, the head loss (in meters, up to one decimal place) per km length due to friction would be ____________
The pre-jump Froude Number for a particular flow in a horizontal rectangular channel is 10. The ratio of sequent depth (i.e., post-jump depth to pre-jump depth) is ____________.
A 4 m wide rectangular channel, having bed slope of 0.001 carries a discharge of 16 m^{3}/s. Considering Manning's roughness coefficient = 0.012 and g = 10 m/s^{2}, the category of the channel slope is
A hydraulically efficient trapezoidal channel section has a uniform flow depth of 2 m. The bed width (expressed in m) of the channel is __________
A square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of 20 mm diameter having a velocity of 10 m/s strikes the plate at its mid-point, at an angle of 30° with the vertical. Consider g as 9.81 m/s^{2 }and neglect the self-weight of the plate. The force F (expressed in N) required to keep the plate in its vertical position is _________
A 3 m wide rectangular channel carries a flow of 6 m^{3}/s. The depth of flow at a section P is 0.5 m. A flat-topped hump is to be placed at the downstream of the section P. Assume negligible energy loss between section P and hump, and consider g as 9.81 m/s^{2}. The maximum height of the hump (expressed in m) which will not change the depth of flow at section P is _________
A penstock of 1 m diameter and 5 km length is used to supply water from a reservoir to an impulse turbine. A nozzle of 15 cm diameter is fixed at the end of the penstock. The elevation difference between the turbine and water level in the reservoir is 500 m. Consider the head loss due to friction as 5% of the velocity head available at the jet. Assume unit weight of water = 10 kN/m^{3 }and acceleration due to gravity (g) = 10 m/s^{2}. If the overall efficiency is 80%, power generated (expressed in kW and rounded to nearest integer) is _______________
In a two-dimensional steady flow field, in a certain region of the x-y plane, the velocity component in the x-direction is given by v_{x} = x^{2} and the density varies as $\rho =\frac{1}{x}$ . Which of the following is a valid expression for the velocity component in the y-direction, v_{y} ?
For steady incompressible flow through a closed-conduit of uniform cross-section, the direction of flow will always be :
A circular pipe has a diameter of 1 m, bed slope of 1 in 1000, and Manning’s roughness coefficient equal to 0.01. It may be treated as an open channel flow when it is flowing just full, i.e., the water level just touches the crest. The discharge in this condition is denoted by $ Q_{full} $. Similarly, the discharge when the pipe is flowing half-full, i.e., with a flow depth of 0.5m, is denoted by $ Q_{half} $. The ratio $ Q_{full}/Q_{half} $ is:
Two reservoirs are connected through a 930 m long, 0.3 m diameter pipe, which has a gate valve. The pipe entrance is sharp (loss coefficient= 0.5) and the valve is half-open (loss coefficient = 5.5). The head difference between the two reservoirs is 20 m. Assume the friction factor for the pipe as 0.03 and g =10 m/s^{2}. The discharge in the pipe accounting for all minor and major losses is _________ m^{3}/s.
A hydraulic jump is a 2 m wide rectangular channel which is horizontal and frictionless. The post-jump depth and velocity are 0.8 m and 1 m/s, respectively. The pre-jump velocity is ___________ m/s. (use g = 10 m/s^{2}).
A short reach of a 2 m wide rectangular open channel has its bed level rising in the direction of flow at a slope of 1 in 10000. It carries a discharge of 4 m^{3}/s and its Manning’s roughness coefficient is 0.01. The flow in this reach is gradually varying. At a certain section in this reach, the depth of flow was measured as 0.5 m. The rate of change of the water depth with distance, dy/dx, at this section is ___(use g = 10 m/s^{2})
The drag force, F_{D} on sphere kept in a uniform flow field depends on the diameter of the sphere, D; flow velocity, V; fluid density, $\rho $; and dynamic viscosity,$\mu $. Which of the following options represents the non-dimensional parameters which could be used to analyze this problem ?
The relationship between the length scale ratio (L_{r}) and the velocity scale ratio (V_{r}) in hydraulic models, in which Froude dynamic similarity is maintained, is:
A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in m/s^{2}) at the end of the nozzle is _________
The velocity components of a two dimensional plane motion of a fluid are : $u=\frac{{y}^{3}}{3}+2x-{x}^{2}y\mathrm{and}v=x{y}^{2}-2y-\frac{{x}^{3}}{3}$
The correct statement is:
A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction factor of the pipe is 0.024. The quantity of water discharged into reservoir C is 0.15 m^{3}/s. Considering the acceleration due to gravity as 9.81 m/s^{2} and neglecting minor losses, the discharge (in m^{3}/s) into the reservoir B is ___________.