Question

Question:Given that for a moving mass ${\mathbf{W}}_{\mathbf{kinetic}}=1/2{\mathbf{Mv}}^{\mathbf{2}}$, how fast would a diesel locomotive need to go to equal the energy stored in a 60-Hz,100-MVA ,60 Hz , 2- pole generator spinning at synchronous speed with an of 30 p.u.-s?

Short answer

Answer

The velocity of diesel locomotive, V is$193.72\frac{\text{miles}}{\text{hour}}$ .

Step-by-step solution

Write the given data from the question.

Consider the value of locomotive, M = 80,000 Kg .

Consider the value of supply frequency is 60-Hz.

Consider the value of rated power is$S_{\text{rated}}=100\text{MVA}$.

Consider the no of poles, P = 2 .

Consider the normalised inertia constant is H = 30 P.u.-s .

Step 2: Determine the formula of velocity of diesel locomotive.

Write the formula of velocity of diesel locomotive.

$\mathbf{V}=\mathbf{86}\mathbf{.}\mathbf{60}\frac{\mathbf{m}}{\mathbf{S}}$ …… (1)

Here, m represent the miles and s is seconds.

Determine the value of velocity of diesel locomotive.

Determine the kinetic energy of generator.

${\text{KE}}_{\text{gen}}={\text{HS}}_{\text{rated}}\text{joules}$

Here, KE is Inertia constant and ${\text{S}}_{\text{rated}}$ is rated power.

Substitute 3 for, 100 MVA for${\text{S}}_{\text{rated}}$ in the above equation (1).

For a moving mass kinetic energy,

${\text{W}}_{\text{Kinetic}}=\frac{1}{2}{\text{MV}}^{\text{2}} \text{joules}$ …… (2)

Here, is mass of the body and is the velocity of moving mass.

Now equate the kinetic energy of mass to kinetic energy of generator.

$$\begin{gathered} K{E}_{gen}=W_{kinetic} \\ K{E}_{gen}=\frac{1}{2}M{V}^2 \\ {V}^2=\frac{2K{E}_{gen}}{M} \\ V=\sqrt{\frac{2\left(K{E}_{gen}\right)}{M}} \end{gathered}$$

Substitute 80000 Kg for $3\times {10}^8$ and for${\text{KE}}_{\text{gen}}$ in the above equation.

$$\begin{gathered} V=\sqrt{\frac{2\left({\text{KE}}_{\text{gen}}\right)}{\text{M}}} \\ =\sqrt{\frac{2\left(3\times {10}^6\right)}{80,000}} \\ =\sqrt{7.5\times {10}^3} \\ =86.60\frac{\text{m}}{\text{S}} \end{gathered}$$

Convert the velocity of the locomotive into miles per hour.

As we know that

$$\begin{gathered} \text{1}\text{mile}=1609.34\text{m} \\ \text{1}\text{m}=\frac{1\text{mile}}{1609.34} \\ \text{1}\text{mile}=1609.34\text{m} \\ \text{1}\text{m}=\frac{1\text{mile}}{1609.34} \end{gathered}$$

Now, determine the velocity of diesel locomotive.

Substitute $\frac{\text{1}\text{mile}}{1609.34}$ for and $\frac{\text{1}\text{hour}}{3600}$ for into equation (1).