Recent questions tagged fluid-mechanics / GO Mechanical

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GATE2017 ME-1: 30
The velocity profile inside the boundary layer for flow over a flat plate is given as $\dfrac{u}{U_{\infty }}= \sin \left ( \dfrac{\Pi }{2}\dfrac{y}{\delta } \right )$, where $U_{\infty}$ is the free stream velocity and $\delta$ is the local boundary layer thickness. If $\delta^{*}$ is ... $\dfrac{2}{\Pi } \\$ $1-\dfrac{2}{\Pi } \\$ $1+\dfrac{2}{\Pi } \\$ $0$

The velocity profile inside the boundary layer for flow over a flat plate is given as $\dfrac{u}{U_{\infty }}= \sin \left ( \dfrac{\Pi }{2}\dfrac{y}{\delta } \right )$, w...

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GATE2017 ME-1: 9
Which one of the following is NOT a rotating machine? Centrifugal pump Gear pump Jet pump Vane pump

Which one of the following is NOT a rotating machine?Centrifugal pumpGear pumpJet pumpVane pump

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GATE2017 ME-1: 8
Water (density $= 1000 kg/m^{3}$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $1 kg/s$. If the pressure drop across the pipe is $100$ KPa, the minimum power required to pump the water across the pipe, in watts, is ______.

Water (density $= 1000 kg/m^{3}$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $1 kg/s$. If the pressure drop across the...

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GATE2017 ME-1: 7
Consider the two-dimensional velocity field given by $\overrightarrow{V}=(5+a_{1}x+b_{1}y)\hat{i}+(4+a_{2}x+b_{2}y)\hat{j}$, where $a_{1}, b_{1}, a_{2}$ and $b_{2}$ are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible? $a_{1}+b_{1}=0$ $a_{1}+b_{2}=0$ $a_{2}+b_{2}=0$ $a_{2}+b_{1}=0$

Consider the two-dimensional velocity field given by $\overrightarrow{V}=(5+a_{1}x+b_{1}y)\hat{i}+(4+a_{2}x+b_{2}y)\hat{j}$, where $a_{1}, b_{1}, a_{2}$ and $b_{2}$ are c...

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GATE2017 ME-1: 6
For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE? ... the flow is fully developed. It is constant but is always lower than the average velocity in the fully developed region.

For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one ...

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GATE2016-3-44
Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enthalpy (in $kJ/kg$) is __________

Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enth...

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GATE2016-3-41
For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vectors in the $x-y$ Cartesian coordinate system. Identify the CORRECT statements from below. The flow is incompressible. The flow is ... $(2)$ and $(3)$ $(1)$ and $(3)$ $(1)$ and $(2)$ $(3)$ and $(4)$

For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vec...

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GATE2016-3-40
The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000 \: kg/m^3$. Acceleration due to gravity $g=10 \: m/s^2$.

The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses ...

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GATE2016-3-39
Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial location of $R/2$ from the centerline of the pipe is $U_1$, the shear stress at the wall is $KμU_1$/$R$, where $K$ is __________

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial l...

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GATE2016-3-16
Grashof number signifies the ratio of inertia force to viscous force buoyancy force to viscous force buoyancy force to inertia force inertia force to surface tension force

Grashof number signifies the ratio ofinertia force to viscous forcebuoyancy force to viscous forcebuoyancy force to inertia forceinertia force to surface tension force

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GATE2016-3-14
For a certain two-dimensional incompressible flow, velocity field is given by $2xy\hat{i}-y^2\hat{j}$ . The streamlines for this flow are given by the family of curves $x^2y^2 = \text{constant}$ $xy^2 = \text{constant}$ $2xy − y^2 \text{constant}$ $xy = \text{constant}$

For a certain two-dimensional incompressible flow, velocity field is given by $2xy\hat{i}-y^2\hat{j}$ . The streamlines for this flow are given by the family of curves$...

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GATE2016-3-13
A channel of width $450$ $mm$ branches into two sub-channels having width $300$ $mm$ and $200$ $mm$ as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $0.9$ $m^3/s$ and the velocity ... velocity in the sub-channel of width $300$ $mm$ is _____________ $m/s$. Assume both inlet and outlet to be at the same elevation.

A channel of width $450$ $mm$ branches into two sub-channels having width $300$ $mm$ and $200$ $mm$ as shown in figure. If the volumetric flow rate (taking unit depth) of...

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GATE2016-2-52
The surface irregularities of electrodes used in an electrochemical machining (ECM) process are $3 \: μm$ and $6 \: μm$ as shown in the figure. If the work-piece is of pure iron and $12V \: DC$ ... $F_e^{+2}$ and the Faraday constant to be $96500$ Coulomb.

The surface irregularities of electrodes used in an electrochemical machining (ECM) process are $3 \: μm$ and $6 \: μm$ as shown in the figure. If the work-piece is of ...

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GATE2016-2-53
For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$ $H=(R+r)+(D+r)$ $H=(R+r)+\sqrt{D^2-R^2}$ $H=(R+r)+\sqrt{2D(R+r)-D^2}$

For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$$H=(R+r)+(D+r)$$H=(R+r)+\sqrt{D^2-R^2}$$H=(R+r)+\sq...

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GATE2016-2-44
A piston-cylinder device initially contains $0.4 \: m^3$ of air (to be treated as an ideal gas) at $100 \: kPa$ and $80^ \circ C$. The air is now isothermally compressed to $0.1 \: m^3$. The work done during this process is ________ $kJ$.

A piston-cylinder device initially contains $0.4 \: m^3$ of air (to be treated as an ideal gas) at $100 \: kPa$ and $80^ \circ C$. The air is now isothermally compressed ...

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GATE2016-2-39
The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $45$ percent of its volume is in oil while the rest is in water. The density of the body is _________ $kg/m^3$. The specific gravity of oil is $0.7$ and density of water is $1000$ $kg/m^3$. Acceleration due to gravity $g$ = $10$ $m/s^2$.

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $45$ percent of its volume is in oil while th...

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GATE2016-2-41
Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $2R \times L$ at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius $R$. The tank is filled with a liquid of density $\rho$ up to the tip ... $2\rho R^2gL(1+\dfrac{\pi }{4}) \\$ $\pi R^2\rho gL \\$ $\dfrac{\pi }{2}\rho R^2gL$

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $2R \times L$ at the bottom of an open tank as shown in the figure. The he...

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GATE2016-2-40
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary bottom plate at a speed of $3\: m/s$. The flow between the plates is solely due to the motion of the top plate. The ... $N/m^2$. Viscosity of the fluid $μ = 0.44 \:kg/m-s$ and density $\rho = 888 \: kg/m^3$.

Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary...

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GATE2016-2-21
In the phase diagram shown in the figure, four samples of the same composition are heated to temperatures marked by $a, b, c$ and $d$. At which temperature will a sample get solutionized the fastest? $a$ $b$ $c$ $d$

In the phase diagram shown in the figure, four samples of the same composition are heated to temperatures marked by $a, b, c$ and $d$.At which temperature will a sample g...

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GATE2016-2-15
A hollow cylinder has length $L$, inner radius $r_1$, outer radius $r_2$, and thermal conductivity $k$. The thermal resistance of the cylinder for radial conduction is $\dfrac{\ln(r_2/r_1)}{2\pi kL} \\$ $\dfrac{\ln(r_1/r_2)}{2\pi kL} \\$ $\dfrac{2\pi kL}{\ln(r_2/r_1)} \\$ $\dfrac{2\pi kL}{\ln(r_1/r_2)}$

A hollow cylinder has length $L$, inner radius $r_1$, outer radius $r_2$, and thermal conductivity $k$. The thermal resistance of the cylinder for radial conduction is$\d...

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GATE2016-2-6
A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is $-2MV \cos\theta \hat{j}$ $2MV \sin\theta \hat{j}$ $2MV \cos\theta \hat{j}$ $-2MV \sin\theta \hat{j}$

A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with ...

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GATE2016-2-13
The volumetric flow rate (per unit depth) between two streamlines having stream functions $\Psi _1$ and $\Psi _2$ is $\mid \Psi _1+\Psi _2\mid$ $\Psi _1\Psi _2$ $\Psi _1/\Psi _2$ $\mid\Psi _1-\Psi _2\mid$

The volumetric flow rate (per unit depth) between two streamlines having stream functions $\Psi _1$ and $\Psi _2$ is$\mid \Psi _1+\Psi _2\mid$$\Psi _1\Psi _2$$\Psi _1/\Ps...

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GATE2016-1-44
A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kinematic viscosity,$v=30\times 10^{-6}$ $m^2/s$, the thermal boundary layer thickness (in $mm$) at $0.5 \:m$ from the leading edge is __________

A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kine...

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GATE2016-1-40
Oil (kinematic viscosity, $v_{\text{oil}}=1.0\times 10^{-5} \:m^2/s$) flows through a pipe of $0.5$ $m$ diameter with a velocity of $10$ $m/s$. Water (kinematic viscosity, $v_w=0.89\times 10^{-6}\:m^2/s$) is flowing through a model pipe of diameter $20 \:mm$. For satisfying the dynamic similarity, the velocity of water (in $m/s$) is __________

Oil (kinematic viscosity, $v_{\text{oil}}=1.0\times 10^{-5} \:m^2/s$) flows through a pipe of $0.5$ $m$ diameter with a velocity of $10$ $m/s$. Water (kinematic viscosity...

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GATE2016-1-17
Propane ($C_3H_8$) is burned in an oxygen atmosphere with $10$% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of $CO$ in the products is __________.

Propane ($C_3H_8$) is burned in an oxygen atmosphere with $10$% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, t...

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GATE2016-1-14
For a floating body, buoyant force acts at the centroid of the floating body center of gravity of the body centroid of the fluid vertically below the body centroid of the displaced fluid

For a floating body, buoyant force acts at thecentroid of the floating bodycenter of gravity of the bodycentroid of the fluid vertically below the bodycentroid of the dis...

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GATE2016-1-13
The instantaneous stream-wise velocity of a turbulent flow is given as follows: $u(x,y,z,t)=\overline{u}(x,y,z)+{u}'(x,y,z,t)$ The time-average of the fluctuating velocity ${u}'(x,y,z,t)$ is $\displaystyle{\frac{u'}{2}} \\$ $\displaystyle{\frac{-\overline{u}}{2}} \\$ $\text{zero}\\$ $\displaystyle{\frac{\overline{u}}{2}}$

The instantaneous stream-wise velocity of a turbulent flow is given as follows:$u(x,y,z,t)=\overline{u}(x,y,z)+{u}'(x,y,z,t)$The time-average of the fluctuating velocity ...

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GATE2015-3-36
A Prandtl tube (Pitot-static tube with $C$=$1$) is used to measure the velocity of water. The differential manometer reading is $10$ $mm$ of liquid column with a relative density of $10$. Assuming $g$ = $9.8$ $m$/$s^2$, the velocity of water (in $m/s$) is ________

A Prandtl tube (Pitot-static tube with $C$=$1$) is used to measure the velocity of water. The differential manometer reading is $10$ $mm$ of liquid column with a relative...

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GATE2015-3-23
A rigid container of volume $0.5 m^3$ contains $1.0$ kg of water at $12^\circ C$ $(v_f = 0.00106 m^3/kg$, $v_g= 0.8908 m^3/kg)$. The state of water is compressed liquid saturated liquid a mixture of saturated liquid and saturated vapor superheated vapor

A rigid container of volume $0.5 m^3$ contains $1.0$ kg of water at $12^\circ C$ $(v_f = 0.00106 m^3/kg$, $v_g= 0.8908 m^3/kg)$. The state of water iscompressed liquidsat...

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GATE2015-3-22
Three parallel pipes connected at the two ends have flow-rates $Q_1$, $Q_2$ and $Q_3$ respectively, and the corresponding frictional head losses are $h_{L1}$, $h_{L2}$ and $h_{L3}$ respectively. The correct expressions for total flow rate $(Q)$ and frictional head loss across the two ends ($h_L$) ... $Q = Q_1 = Q_2 = Q_3; h_L = h_{L1} = h_{L2} = h_{L3}$

Three parallel pipes connected at the two ends have flow-rates $Q_1$, $Q_2$ and $Q_3$ respectively, and the corresponding frictional head losses are $h_{L1}$, $h_{L2}$ an...

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GATE2015-3-9
Couette flow is characterized by steady, incompressible, laminar flow through a straight circular pipe fully developed turbulent flow through a straight circular pipe steady, incompressible, laminar flow between two fixed parallel plates steady, incompressible, laminar flow between one fixed plate and the other moving with a constant velocity

Couette flow is characterized bysteady, incompressible, laminar flow through a straight circular pipefully developed turbulent flow through a straight circular pipesteady...

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GATE2015-2-41
For a fully developed laminar flow of water (dynamic viscosity $0.001$ $P_{a-s}$) through a pipe of radius $5$ $cm$, the axial pressure gradient is −$10$ $Pa/m$. The magnitude of axial velocity (in $m/s$) at a radial location of $0.2$ $cm$ is _______

For a fully developed laminar flow of water (dynamic viscosity $0.001$ $P_{a-s}$) through a pipe of radius $5$ $cm$, the axial pressure gradient is −$10$ $Pa/m$. The ma...

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GATE2015-2-40
The head loss for a laminar incompressible flow through a horizontal circular pipe is $h_1$. Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is $h_2$. The ratio $h_2$/$h_1$ is $1$ $4$ $8$ $16$

The head loss for a laminar incompressible flow through a horizontal circular pipe is $h_1$. Pipe length and fluid remaining the same, if the average flow velocity double...

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GATE2015-2-15
If a foam insulation is added to a $4 \: cm$ outer diameter pipe as shown in the figure, the critical radius of insulation (in $cm$) is _____________

If a foam insulation is added to a $4 \: cm$ outer diameter pipe as shown in the figure, the critical radius of insulation (in $cm$) is _____________

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GATE2015-2-14
Within a boundary layer for a steady incompressible flow, the Bernoulli equation holds because the flow is steady holds because the flow is incompressible holds because the flow is transitional does not hold because the flow is frictional

Within a boundary layer for a steady incompressible flow, the Bernoulli equationholds because the flow is steadyholds because the flow is incompressibleholds because the ...

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GATE2015-2-12
If the fluid velocity for a potential flow is given by $V(x,y)=u(x,y)i+v(x,y)j$ with usual notations, then the slope of the potential line at $(x,y)$ is $\dfrac{v}{u} \\$ $-\dfrac{u}{v} \\$ $\dfrac{u^2}{v^2} \\$ $\dfrac{u}{v}$

If the fluid velocity for a potential flow is given by $V(x,y)=u(x,y)i+v(x,y)j$ with usual notations, then the slope of the potential line at $(x,y)$ is$\dfrac{v}{u} \\$$...

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GATE2015-1-49
The velocity field of an incompressible flow is given by $V=(a_1x+a_2y+a_3z)i+(b_1x+b_2y+b_3z)j+(c_1x+c_2y+c_3z)z$, where $a_1$ = $2$ and $c_3$ = − $4$. The value of $b_2$ is ___________

The velocity field of an incompressible flow is given by $V=(a_1x+a_2y+a_3z)i+(b_1x+b_2y+b_3z)j+(c_1x+c_2y+c_3z)z$, where $a_1$ = $2$ and $c_3$ = − $4$. The value of $b...

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GATE2015-1-53
Water $(\rho = 1000 \: kg/m^3)$ flows through a venturimeter with inlet diameter $80 \: mm$ and throat diameter $40 \: mm$. The inlet and throat gauge pressures are measured to be $400 \: kPa$ and $130 \: kPa$ respectively. Assuming the venturimeter to be horizontal and neglecting friction, the inlet velocity (in $m/s$) is _______

Water $(\rho = 1000 \: kg/m^3)$ flows through a venturimeter with inlet diameter $80 \: mm$ and throat diameter $40 \: mm$. The inlet and throat gauge pressures are measu...

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GATE2015-1-48
Match the following pairs: \begin{array}{|l|l|l|l|} \hline &\textbf{Equation} && \textbf{Physical Interpretation} \\ \hline P. & \nabla \times \overrightarrow{V}=0 & I. & \text{ Incompressible continuity equation} \\ \hline Q. & \nabla \bullet \overrightarrow{V}=0 & II. ... $P-IV, Q-III, R-I, S-II$ $P-III, Q-I, R-IV, S-II$ $P-III, Q-I, R-II, S-IV$

Match the following pairs:\begin{array}{|l|l|l|l|} \hline &\textbf{Equation} && \textbf{Physical Interpretation} \\ \hline P. & \nabla \times \overrightarrow{V}=0 & I. & ...

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GATE2015-1-47
For flow through a pipe of radius $R$, the velocity and temperature distribution are as follows: $u(r,x)=C_1,$, and $T(r,x)=C_2[1- \left (\dfrac{r}{R} \right )^3]$ where $C_1$ and $C_2$ ... mean velocity of flow. The value of $T_m$ is $\dfrac{0.5C_2}{U_m} \\$ $0.5C_2 \\$ $0.6C_2 \\$ $\dfrac{0.6C_2}{U_m}$

For flow through a pipe of radius $R$, the velocity and temperature distribution are as follows:$u(r,x)=C_1,$, and $T(r,x)=C_2[1- \left (\dfrac{r}{R} \right )^3]$ where $...

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