# Two additional authored calculation exercises

Subject: Disaster Management

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/dm/#tee/practice/calculations/extra-exercises

Canonical: https://deep-learning-study-room.vercel.app/read/dm/tee/practice/calculations--extra-exercises/

Supplementary worked examples · no numerical question found in the available 12 TEE sittings

Added runoff and magnitude exercises. Their numbers and question selection were written for practice; this is not a recovered paper or a confirmed M2/TEE composition.

### Illustrative calculation (not a PYQ). A catchment has C = 0.6, I = 50 mm/h and area = 0.5 km². Estimate peak runoff in m³/s using the rational method.

#### Answer

## Given

| Given | Value |
| --- | --- |
| Runoff coefficient C | 0.6 |
| Rainfall intensity I | 50 mm/h |
| Catchment area A | 0.5 km² |

## To find

Estimated peak runoff Q in m³/s.

## Formula and why



$$
Q=0.27778CIA
$$



The factor converts mm/h over km² to m³/s. Assume the rainfall intensity and catchment meet the rational-method assumptions.

## Step-by-step solution

#### Step 1. Multiply coefficient and intensity



$$
0.6\times50=30
$$



#### Step 2. Multiply by catchment area



$$
30\times0.5=15
$$



#### Step 3. Convert to discharge



$$
Q\approx0.27778\times15=4.1667\,\mathrm{m^3/s}
$$



**Final answer:** Approximately 4.17 m³/s.

#### Illustrative application · Two catchments in the same rain

A paved catchment can send a larger fraction of rainfall into rapid runoff than a more permeable one. In a rational-method problem, this appears through the runoff coefficient C; keep the area and rainfall units consistent before calculating discharge.

### Illustrative calculation (not a PYQ). Two earthquakes have magnitudes 6 and 5. Find the amplitude ratio and approximate energy ratio.

#### Answer

## Given

| Quantity | Value |
| --- | --- |
| Larger magnitude | 6 |
| Smaller magnitude | 5 |

## To find

Larger-to-smaller amplitude and energy ratios.

## Formula and why



$$
A_2/A_1=10^{\Delta M},\qquad E_2/E_1\approx10^{1.5\Delta M}
$$



Magnitude is logarithmic. The energy relation has a different exponent from the amplitude relation.

## Step-by-step solution

#### Step 1. Calculate magnitude difference



$$
\Delta M=6-5=1
$$



#### Step 2. Calculate amplitude ratio



$$
10^1=10
$$



#### Step 3. Calculate energy ratio



$$
10^{1.5\times1}=10^{1.5}\approx31.62
$$



**Final answer:** Amplitude ratio 10:1; approximate energy ratio 31.62:1.

#### Illustrative application · Same magnitude, different local effects

One earthquake has a source magnitude, but a nearby settlement with vulnerable buildings may experience stronger damaging effects than a distant settlement on firm ground. A one-unit magnitude difference means a tenfold amplitude ratio in the stated logarithmic comparison; it does not mean ten times the damage.