Bernoulli’s equation is applicable for
For a steady incompressible laminar flow between two infinite parallel stationary plates the shear stress variation is
A traingular pipe network is shown in the figure.
The head loss in each pipe is given by h_{f}=rQ^{1.8}, with the variable expressed in a consistent set of units. The value of r for the pipe AB is 1 and for the pipe BC is 2. If the discharge suplied at the point A (i.e. 100) is equally divided between the pipe AB and AC, the value of r (up to two decimal places) for the pipe AC should be _____________
A 1 m wide rectangular channel has a bed slope of 0.0016 and the Manning's roughness cofficient is 0.04. Uniform flow takes place in the channel at a flow depth of 0.5 m. At a particular section, gradually varied flow (GVF) is observed and the flow depth is measured as 0.6 m. The GVF profile at that section is classified as
Water flows through a $90^\circ$ bend in a horizontal plane as depicted in the figure.
A pressure of 140 kPa is mesaured at section 1-1. The inlet diameter marked at section 1-1 is $\frac{27}{\sqrt{\mathrm\pi}}$cm, while the nozzle diameter marked at section 2-2 is $\frac{14}{\sqrt{\mathrm\pi}}$cm. Assume the following.
(i) Acceleration due to gravity = 10 m/s^{2}
(ii) Weights of both the bent pipe segment as well as water are negligible.
(iii) Friction across the bend is negligible.
The magnitude of the force (in kN, up two decimal places) that would be required to hold the pipe section is _____________
The figure shows a U-tube having a 5 mm × 5 mm square cross-section filled with mercury (specific gravity=13.6) up to a height of 20 cm in each limb (open to the atmosphere).
If $ 5\;cm^3 $ of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in LEFT limb will be _____________
A sector gate is provided on a spillway as shown in the figure. Assuming g = 10 m/s^{2}, the resultant force per meter length (expressed in kN/m) on the gate will be __________
Group I contains the types of fluids while Group II contains the shear stress - rate of shear relationship of different types of fluids, as shown in the figure.
The correct match between Group I and Group II is
An incompressible homogeneous fluid is flowing steadily in a variable diameter pipe having the large and small diameters as 15 cm and 5 cm, respectively. If the velocity at a section at the 15 cm diameter portion of the pipe is 2.5 m/s, the velocity of the fluid (in m/s) at a section falling in 5 cm portion of the pipe is ___________
The dimension for kinematic viscosity is
A particle moves along a curve whose parametric equations are: $x={t}^{3}+2t,y=-3{e}^{-2t}$ and $z=2\mathrm{sin}\left(5t\right)$ where x,y and z show variations of the distance covered by the particle (in cm) with time t (in s). The magnitude of the acceleration of the particle (in cm/s^{2}) at t=0 is ________
A horizontal jet of water with its cross-sectional area of 0.0028 m^{2} hits a fixed vertical plate with a velocity of 5 m/s. After impact the jet splits symmetrically in a plane parallel to the plane of the plate. The force of impact (in N) of the jet on the plate is
A venturimeter, having a diameter of 7.5 cm at the throat and 15 cm at the enlarged end, is installed in a horizontal pipeline of 15 cm diameter. The pipe carries an incompressible fluid at a steady rate of 30 litres per second. The difference of pressure head measured in terms of the moving fluid in between the enlarged and the throat of the venturimeter is observed to be 2.45 m. Taking the acceleration due to gravity as 9.81 m/s^{2}, the coefficient of discharge of the venturimeter (correct up to two places of decimal) is ______________
Three rigid buckets, shown as in the figures (1), (2) and (3), are of identical heights and base areas. Further, assume that each of these buckets have negligible mass and are full of water. The weights of water in these buckets are denoted as W_{1}, W_{2}, and W_{3} respectively. Also, let the force of water on the base of the bucket be denoted as F_{1}, F_{2}, and F_{3} respectively. The option giving an accurate description of the system physics is
An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d_{1} and d_{2} (where d_{1} = 4d_{2}) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________
A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0.21 m^{3}/s. Allowable velocity through the main is 0.75 m/s. Assume f = 0.01, g = 9.81 m/s^{2}. The minimum gradient (in cm/100 m length) to be given to this gravity main so that the required amount of water flows without any difficulty is ___________
A plane flow has velocity components $u=\frac{x}{{T}_{1}},v=-\frac{y}{{T}_{2}}$ and w=0 along x,y and z directions respectively, where ${T}_{1}\left(\ne 0\right)and{T}_{2}\left(\ne 0\right)$ are constants having the dimension of time. The given flow is incompressible if
Group I lists a few devices while Group II provides information about their uses. Match the devices with their corresponding use.
A horizontal nozzle of 30 mm diameter discharges a steady jet of water into the atmosphere at a rate of 15 litres per second. The diameter of inlet to the nozzle is 100 mm. The jet impinges normal to a flat stationary plate held close to the nozzle end. Neglecting air friction and considering the density of water as 1000 kg/m^{3}, the force exerted by the jet (in N) on the plate is _________
A venturimeter having a throat diameter of 0.1 m is used to estimate the flow rate of a horizontal pipe having a diameter of 0.2 m. For an observed pressure difference of 2 m of water head and coefficient of discharge equal to unity, assuming that the energy losses are negligible, the flow rate (in m^{3}/s) through the pipe is approximately equal to
With reference to a standard Cartesian (x, y) plane, the parabolic velocity distribution profile of fully developed laminar flow in x-direction between two parallel, stationary and identical plates that are separated by distance, h, is given by the expression
In this equation, the y = 0 axis lies equidistant between the plates at a distance h/2 from the two plates, p is the pressure variable and μ is the dynamic viscosity term. The maximum and average velocities are, respectively
For subcritical flow in an open channel, the control section for gradually varied flow profiles is
Group-I contains dimensionless parameters and Group- II contains the ratios.
The correct match of dimensionless parameters in Group- I with ratios in Group-II is:
For a two dimensional flow field, the stream function $\Psi $ is given as $\Psi =\frac{3}{2}({y}^{2}-{x}^{2})$.The magnitude of discharge occurring between the stream lines passing through points (0,3) and (3,4) is:
A 2 km long pipe of 0.2 m diameter connects two reservoirs. The difference between water levels in the reservoirs is 8 m. The Darcy-Weisbachfriction factor of the pipe is 0.04. Accounting for frictional, entry and exit losses, the velocity in the pipe (in m/s) is:
The normal depth in a wide rectangular channel is increased by 10%. The percentage increase in the discharge in the channel is:
If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p, then the maximum shear stress developed inside the cube is
A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed slope is 0.002. The channel is lined with smooth concrete (Manning’s n = 0.012). The hydraulic radius (in m) for a depth of flow of 3.0 m is
A rectangular open channel of width 5.0 m is carrying a discharge of 100 m^{3}/s. The Froude number of the flow is 0.8. The depth of flow (in m) in the channel is
The circular water pipes shown in the sketch are flowing full. The velocity of flow (in m/s) in the branch pipe “R” is
For a given discharge, the critical flow depth in an open channel depends on
For a body completely submerged in a fluid, the centre of gravity(G) and centre of Buoyancy (O) are known. The body is considered to be in stable equilibrium if
The flow in a horizontal, frictionless rectangular open channel is supercritical. A smooth hump is built on the channel floor. As the height of hump is increased, choked condition is attained. With further increase in the height of the hump, the water surface will
A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m in their water levels. The pipe is to be replaced by two pipes of the same length and equal diameter d to convey 25% more discharge under the same head loss. If the friction factor is assumed to be the same for all the pipes, the value of d is approximately equal to which of the following options?
A spillway discharges flood at a rate of 9 m^{3}/s per metre width. If the depth of flow on the horizontal apron at the toe of the spillway is 46 cm, the tail water depth needed to form a hydraulic jump is approximately given by which of the following?
A mild-sloped channel is followed by a steep-sloped channel. The profiles of gradually varied flow in the channel are
The flow in a rectangular channel is subcritical.if the width of the channel is reduced at a certain section, the water surface under no-choke condition will
Group-I gives a list of devices and Group-II the list of uses
For a rectangular channel section, Group I lists geometrical elements and Group II gives proportions for hydraulically efficient section.
y_{e} is the follow depth corresponding to hydraulically efficient section. The correct match of Group I with Group II is
The Froude number of flown in a rectangular channel is 0.8. If the depth of flow is 1.5 m, the critical depth is
Direct step method of computation for gradually varied flow is
Water flows through a 100 mm diameter pipe with a velocity of 0.015 m/sec. If the kinematic viscosity of water is 1.13 × 10^{-6} m^{2}/sec, the friction factor of the pipe material is
A rectangular open channel of width 4.5m is carrying a discharge of 100 m^{3}/sec. The critical depth of the channel is
Water ($\gamma $_{w} = 9.879 kN/m^{3}) flows with a flow rate of 0.3 m^{3}/sec through a pipe AB of 10m length and of uniform cross section. The end ‘B’ is above end ‘A’ and the pipe makes an angle of 30º to the horizontal. For a pressure of 12 kN/m^{2} at the end ‘B’, the corresponding pressure at the end ‘A’ is
A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water surface in not traveling up-stream. This is because the flow in the canal is
The flow of water (mass density = 1000 kg/m^{3 }and kinematic viscosity = 10^{-6} m^{2}/s) in a commercial pipe, having equivalent roughness ks as 0.12 mm, yields an average shear stress at the pipe boundary = 600 N/m^{2}. The value of ks/${\mathrm{\delta}}^{\text{'}}$ (${\mathrm{\delta}}^{\text{'}}$ being the thickness of laminar sub-layer) for this pipe is
A river reach of 2.0 km long with maximum flood discharge of 10000 m^{3}/s is to be physically modeled in the laboratory where maximum available discharge is 0.20 m^{3}/s. For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is
A rectangular channel 6.0 m wide carries a discharge of 16.0m^{3}/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.
The longitudinal slope of the channel is
A hump is to be provided on the channel bed. The maximum height of the hump without affecting the upstream flow condition is
The channel width is to be contracted. The minimum width to which the channel can be contracted without affecting the upstream flow condition is
An automobile with projected area 2.6 m^{2} is running on a road with speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m^{3} and 1.5 × 10^{-5 }m^{2}/s, respectively. The drag coefficient is 0.30.
The drag force on the automobile is
The metric horse power required to overcome the drag force is
There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate?
At two points 1 and 2 in a pipeline the velocities and V and 2V, respectively. Both the points are at the same elevation. The fluid density is $\mathrm{\rho}$. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P_{1} and P_{2} at poiunts 1 and 2 is
A horizontal water jet with a velocity of 10 m/s and cross sectional area of 10 mm^{2} strikes a flat plate held normal to the flow direction. The density of water is 1000 kg/m^{3}. The total force on the plate due to the jet is
A 1: 50 scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 1000 m^{3}/s. The discharge to be maintained in the model test is
A triangular open channel has a vertex angle to 90° and carries flow at a critical depth of 0.30 m. The discharge in the channel is
Flow rate of a fluid (density = 1000 kg/m^{3}) in a small diameter tube is 800 mm^{3}/s. The length and the diameter of the tube are 2 m and 0.5 mm, respectively. The pressure drop in 2 m length is equal to 2.0 MPa. The viscosity of the fluid is
The flow rate in a wide rectangular open channel is 2.0 m^{3}/s per metre width. The channel bed slope is 0.002. The Manning’s roughness coefficient is 0.012. The slope of the channel is classified as
A rectangular open channel needs to be designed to carry a flow of 2.0 m^{3}/s under uniform flow conditions. The Manning’s roughness coefficient is 0.018. The channel should be such that the flow depth is equal to half the width, and the Froude number is equal to 0.5.
The bed slope of the channel to be provided is
Keeping the width, flow depth and roughness the same, if the bed slope of the above channel is doubled, the average, boundary shear stress under uniform flow conditions is