Potential function $$\phi $$ is given as $$\phi $$ = x<sup>2</sup> - y<sup>2</sup>. What will be the stream function $$\psi $$ with the condition $$\psi $$ = 0 at x = y = 0?

A particle of mass m is confined in the potential
Quantum Mechanics mcq question image

\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

A

$$\frac{{31}}{{10}}\hbar \omega $$

B

$$\frac{{25}}{{10}}\hbar \omega $$

C

$$\frac{{13}}{{10}}\hbar \omega $$

D

$$\frac{{11}}{{10}}\hbar \omega $$

If $${\text{W}} = \phi + {\text{i}}\psi $$ represents the complex potential for an electric field. Given $$\psi = {{\text{x}}^2} - {{\text{y}}^2} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}},$$ then the function $$\phi $$ is

A

$$ - 2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$

B

$$2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$

C

$$ - 2{\text{xy}} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$

D

$$2{\text{xy}} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$

The fresh feed to an ammonia synthesis reactor contains nitrogen, hydrogen and 2.0 mole per cent inerts. The molar ratio of H2:N2 is 3:1. The product stream consists of pure ammonia. Since conversion in the reactor is only 15%, a recycle stream is used and in order to avoid build-up of inerts, a purge stream is withdrawn. The rate of purge stream is adjusted to keep inert concentration in the recycle stream at 8 mole per cent. For a fresh feed rate of 100 moles/hr. Note that recycle stream contains only nitrogen, hydrogen and inerts. The N2:H2 ratio of 1:3 is maintained in every process stream, and calculate the moles of nitrogen entering the reactor and in the recycle stream?

A

125 moles/hr, 100.50 moles

B

135 moles/hr, 50 moles

C

125 moles/hr, 50 moles

D

185 moles/hr, 100.50 moles

The fresh feed to an ammonia synthesis reactor contains nitrogen, hydrogen and 2.0 mole per cent inerts. The molar ratio of H2:N2 is 3:1. The product stream consists of pure ammonia. Since conversion in the reactor is only 15%, a recycle stream is used and in order to avoid build-up of inerts, a purge stream is withdrawn. The rate of purge stream is adjusted to keep inert concentration in the recycle stream at 8 mole per cent. For a fresh feed rate of 100 moles/hr. Note that recycle stream contains only nitrogen, hydrogen and inerts. The N2:H2 ratio of 1:3 is maintained in every process stream, and calculate the number of moles, moles of inerts and moles of hydrogen in the recycle stream?

A

437 moles/hr, 35 moles/hr, 301.5 moles/hr

B

237 moles/hr, 30 moles/hr, 200 moles/hr

C

567 moles/hr, 35 moles/hr, 205 moles/hr

D

347 moles/hr, 30 moles/hr, 500 moles/hr

S = Training data = => No (negative example). How will S be represented after encountering this training data?

A

B

C

D

The value of $$\left( {\frac{{\sin \theta + \sin \phi }}{{\cos \theta + \cos \phi }} + \frac{{\cos \theta - \cos \phi }}{{\sin\theta - \sin\phi }}} \right)$$ is?

A

1

B

2

C

$$\frac{1}{2}$$

D

0

If the electrostatic potential were Igiven by $$\phi = {\phi _0}$$ (x² + y² + z²), where $${\phi _0}$$ is constant, then the charge density giving rise to the above potential would be

A

zero

B

$$ - 6\,{\phi _0}{\varepsilon _0}$$

C

$$ - 2\,{\phi _0}{\varepsilon _0}$$

D

$$ - \frac{{6\,{\phi _0}}}{{{\varepsilon _0}}}$$

The fresh feed to an ammonia synthesis reactor contains nitrogen, hydrogen and 2.0 mole per cent inerts. The molar ratio of H2:N2 is 3:1. The product stream consists of pure ammonia. Since conversion in the reactor is only 15%, a recycle stream is used and in order to avoid build-up of inerts, a purge stream is withdrawn. The rate of purge stream is adjusted to keep inert concentration in the recycle stream at 8 mole per cent. For a fresh feed rate of 100 moles/hr. Note that recycle stream contains only nitrogen, hydrogen and inerts. The N2:H2 ratio of 1:3 is maintained in every process stream. Calculate the moles of ammonia produced.

A

38.90 moles/hr

B

28.90 moles/hr

C

37.50 moles/hr

D

27.50 moles/hr

Consider the following remarks pertaining to the irrotational flow: 1. The Laplace equation of stream function $\frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {y^2}}} = 0$ must be satisfied for the flow to be potential. 2. The Laplace equation for the velocity potential $\frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {y^2}}} = 0$ must be satisfied to fulfil the orate . of mass conservation i.e continuity equation.. Which of the above statements is/are correct?

A

1 only

B

Both 1 and 2

C

2 only

D

Neither 1 or 2

The cumulative distribution function for the lognormal distribution is given by _____ \) b) $\phi$ c) $\phi$ d) $\phi$

A

$\phi-\theta}{\omega}]$ \) c) $\phi-\omega}{\omega}]$ d) $\phi-\theta}{\theta}]$ View Answer]

B

\frac{ln⁡(a)-\theta}{\omega}

C

\frac{ln⁡(a)-\theta}{\omega}

D

\frac{ln⁡(a)-\theta}{\omega}

Potential function $$\phi $$ is given as $$\phi $$ = x² - y². What will be the stream function $$\psi $$ with the condition $$\psi $$ = 0 at x = y = 0?

Related Questions

Potential function $$\phi $$ is given as $$\phi $$ = x2 - y2. What will be the stream function $$\psi $$ with the condition $$\psi $$ = 0 at x = y = 0?

Related Questions

Potential function $$\phi $$ is given as $$\phi $$ = x² - y². What will be the stream function $$\psi $$ with the condition $$\psi $$ = 0 at x = y = 0?