Fluid Statics and Conservation Equations - Fluid Mechanics and Mechanical Operations - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2007

Consider a soap film bubble of diameter \(D\). If the external pressure is \(P_o\) and the surface tension of the soap film is \(\sigma\), the expression for the pressure inside the bubble is

A

\(P_o\)

B

\(P_o + \frac{2\sigma}{D}\)

C

\(P_o + \frac{4\sigma}{D}\)

D

\(P_o + \frac{8\sigma}{D}\)

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2

2007 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2007

A pipeline system carries crude oil of density 800 kg/m³. The volumetric flow rate at point 1 is 0.28 m³/s. The cross sectional areas of the branches 1,2 and 3 are 0.012, 0.008 and 0.004 m² respectively. All the three branches are in a horizontal plane and the friction is negligible. If the pressures at the points 1 and 3 are 270 kPa and 240 kPa respectively, then the pressure at point 2 is

A

202 kPa

B

240 kPa

C

284 kPa

D

355 kPa

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3

2007 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2007

The figure shows the idealized view of a return elbow or U bend, which is connected to two pipes by flexible hoses that transmit no force. Water with density 1000 kg/m³ flows at velocity of 10 m/s through the pipe, which has a uniform ID of 0.1m. The gauge pressure at points 1 and 2 are 304 kPa and 253 kPa respectively. The horizontal force F required to keep the elbow in position is

A

1574 N

B

1970 N

C

5942 N

D

7533 N

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4

2008 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2008

Q.9 Three containers are filled with water up to the same height as shown. The pressures at the bottom of the containers are denoted as P1, P2 and P3. Which ONE of the following relationships is true?

A

\(P_3 > P_1 > P_2 \)

B

\(P_2 > P_1 > P_3 \)

C

\(P_1 > P_2 = P_3 \)

D

\(P_1 = P_2 = P_3 \)

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5

2008 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2008

A pump draws oil (specific gravity 0.8) from a storage tank and discharges it to an overhead tank. The mechanical energy delivered by the pump to the fluid is 50 J/kg. The velocities at the suction and the discharge points of the pump are 1 m/s and 7 m/s, respectively. Neglecting friction losses and assuming kinetic energy correction factor to be unity, the pressure developed by the pump (in kN/m\(^2\)) is

A

19.2

B

20.8

C

40

D

80

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6

2008 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2008

A steady flow field of an incompressible fluid is given by \(\vec{V}=(Ax+By)\hat{i}-Ay\hat{j}\), where A = 1 s⁻¹, B = 1 s⁻¹, and x, y are in meters. The magnitude of the acceleration (in m/s²) of a fluid particle at (1, 2) is

A

1

B

√2

C

√5

D

√10

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7

2009 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2009

For an incompressible flow, the \(x\)- and \(y\)- components of the velocity vector are \(v_x = 2(x + y)\); \(v_y = 3(y + z)\) where \(x, y, z\) are in metres and velocities are in m/s. Then the \(z\)-component of the velocity vector (\(v_z\)) of the flow for the boundary condition \(v_z = 0\) at \(z = 0\) is

A

\(5z\)

B

\(-5z\)

C

\(2x + 3z\)

D

\(-2x - 3z\)

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8

2009 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2009

The velocity of water at the tip of the nozzle (in m/s) is

A

13.4

B

18.0

C

23.2

D

27.1

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9

2009 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2009

The gauge pressure (in kPa) at point B is

A

80.0

B

100.0

C

239.3

D

367.6

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10

2010 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2010

The stream function in a x-y plane is given below: \( \psi = \frac{1}{2} x^2 y^3 \) The velocity vector for this stream function is

A

\(x y^3 \hat{i} - \frac{3}{2} x^2 y^2 \hat{j} \)

B

\(\frac{3}{2} x^2 y^2 \hat{i} - x y^3 \hat{j} \)

C

\(\frac{3}{2} x^2 y^2 \hat{i} + x y^3 \hat{j} \)

D

\(x y^3 \hat{i} + \frac{3}{2} x^2 y^2 \hat{j} \)

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11

2010 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2010

The height of a fluidized bed at incipient fluidization is 0.075 m, and the corresponding voidage is 0.38. If the voidage of the bed increases to 0.5, then the height of the bed would be

A

0.058 m

B

0.061 m

C

0.075 m

D

0.093 m

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12

2010 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2010

A hydrometer, with stem cross-sectional area of \( 2.82 \times 10^{-5} \text{ m}^2 \), is immersed in a very large vessel containing water as shown in the figure. The immersed volume is \( 15 \times 10^{-6} \text{ m}^3 \) and the length of the stem above water surface is \( L_w \). If the entire volume of water is replaced by a liquid with specific gravity 1.5 and if the length of the stem above the liquid surface is \( L_l \), then the difference, \( L_l - L_w \), is

A

-177 mm

B

177 mm

C

-266 mm

D

266 mm

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13

2011 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2011

In a thin-walled cylindrical vessel of thickness \(t\) with inside radius \(r\), the internal gauge pressure is \(p\). The hoop stress and the longitudinal stress in the shell are \(\sigma_h\) and \(\sigma_l\) respectively. Which ONE of the following statements is TRUE?

A

\(\sigma_h = \frac{pr}{t}, \sigma_l = \frac{pr}{4t}\)

B

\(\sigma_h = \frac{pr}{4t}, \sigma_l = \frac{pr}{t}\)

C

\(\sigma_h = \frac{pr}{2t}, \sigma_l = \frac{pr}{t}\)

D

\(\sigma_h = \frac{pr}{t}, \sigma_l = \frac{pr}{2t}\)

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14

2011 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2011

Two liquids (P and Q) having same viscosity are flowing through a double pipe heat exchanger as shown in the schematic below. Densities of P and Q are 1000 and 800 kg/m\(^3\) respectively. The average velocities of the liquids P and Q are 1 and 2.5 m/s respectively. The inner diameters of the pipes are 0.31 and 0.1 m. Both pipes are 5 mm thick. The ratio of the Reynolds numbers \( Re_P \) to \( Re_Q \) is

A

2.5

B

1.55

C

1

D

4

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15

2012 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2012

A Newtonian fluid of viscosity \(\mu\) flows between two parallel plates due to the motion of the bottom plate (as shown below), which is moved with a velocity \(V\). The top plate is stationary. The steady, laminar velocity profile in the \(x\)-direction is

A

\(V \left[ \frac{y}{b} \right]\)

B

\(V \left[ \left( \frac{y}{b} \right)^2 - 1 \right]\)

C

\(V \left[ 1 - \left( \frac{y}{b} \right)^2 \right]\)

D

\(V \left[ 1 - \frac{y}{b} \right]\)

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16

2012 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2012

The force per unit area (in the \(x\)-direction) that must be exerted on the bottom plate to maintain the flow is

A

\(\mu V / b\)

B

\(-\mu V / b\)

C

\(2 \mu V / b\)

D

\(-2 \mu V / b\)

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17

2013 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2013

An open tank contains two immiscible liquids of densities (800 kg/m³ and 1000 kg/m³) as shown in the figure. If g = 10 m/s², under static conditions, the gauge pressure at the bottom of the tank in Pa is __________

Check answer

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18

2013 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2013

The apparent viscosity of a fluid is given by \(0.007 \left| \frac{dV}{dy} \right|^{0.3}\) where \(\left| \frac{dV}{dy} \right|\) is the velocity gradient. The fluid is

A

Bingham plastic

B

dilatant

C

pseudoplastic

D

thixotropic

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19

2013 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2013

The mass balance for a fluid with density \(\rho\) and velocity vector \(\vec{V}\) is

A

\(\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{V}) = 0\)

B

\(\frac{\partial \rho}{\partial t} + \vec{V} \cdot (\nabla \rho) = 0\)

C

\(\frac{\partial \rho}{\partial t} + \rho (\nabla \cdot \vec{V}) = 0\)

D

\(\frac{\partial \rho}{\partial t} - \vec{V} \cdot (\nabla \rho) = 0\)

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20

2013 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Fluid Statics and Conservation Equations

Chemical Engineering (CH) 2013

An incompressible Newtonian fluid, filled in an annular gap between two concentric cylinders of radii \(R_1\) and \(R_2\) as shown in the figure, is flowing under steady state conditions. The outer cylinder is rotating with an angular velocity of \(\Omega\) while the inner cylinder is stationary. Given that \((R_2 - R_1) \ll R_1\), the profile of the θ-component of the velocity \(V_θ\) can be approximated by,

A

\(R_1 \Omega\)

B

\(\frac{r - R_1}{R_2 - R_1} r \Omega\)

C

\(\frac{r + R_1}{R_2 + R_1} R_1 \Omega\)

D

\(\frac{r - R_1}{R_2 - R_1} R_1 \Omega\)

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