**Part 1: Elevation Head, Pressure Head, and Total Head**

To calculate the elevation head, pressure head, and total head at each point, follow these steps:

**Elevation Head (H_e):**Measure the vertical distance from each point to the reference point (point a).**Pressure Head (H_p):**Convert the elevation head to pressure head using the following formula: H_p = γ_w * z, where γ_w is the unit weight of water (9.81 kN/m³) and z is the elevation head.**Total Head (H_t):**Sum the elevation head and pressure head for each point.

Here’s the table of elevation head, pressure head, and total head for each point:

Point | Elevation Head (m) | Pressure Head (kN/m²) | Total Head (kN/m²) |
---|---|---|---|

a | 0 | 0 | 0 |

b | 0.8 | 7.85 | 7.85 |

c | 2.0 | 19.62 | 19.62 |

d | 3.5 | 34.34 | 34.34 |

e | 4.2 | 41.31 | 41.31 |

**Part 2: Discharge Velocity and Seepage Velocity**

To calculate the discharge velocity and seepage velocity at each point, follow these steps:

**Discharge Velocity (v_d):**Use Darcy’s law to calculate the discharge velocity: v_d = -k * i, where k is the coefficient of permeability and i is the hydraulic gradient.**Hydraulic Gradient (i):**Calculate the hydraulic gradient by dividing the change in total head by the length of the soil layer.**Seepage Velocity (v_s):**Calculate the seepage velocity by dividing the discharge velocity by the porosity (n) of the soil: v_s = v_d / n.

Here’s the table of discharge velocity and seepage velocity for each point:

Point | Soil | Discharge Velocity (cm/s) | Seepage Velocity (cm/s) |
---|---|---|---|

b | Sand I | 1.67 | 4.2 |

c | Sand I | 1.67 | 4.2 |

d | Sand II | 0.71 | 4.15 |

e | Sand II | 0.71 | 4.15 |

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**Part 3: Quantity of Seepage**

To calculate the quantity of seepage (Q), use the following formula: Q = A * v_d, where A is the cross-sectional area of the soil layer.

For Sand I:

Q = (0.42 m²) * (1.67 cm/s) = (0.42 m²) * (0.0167 m/s) = 0.007 m³/s

For Sand II:

Q = (0.31 m²) * (0.71 cm/s) = (0.31 m²) * (0.0071 m/s) = 0.0022 m³/s

Therefore, the total quantity of seepage is the sum of the seepage in Sand I and Sand II:

Q_total = Q_Sand_I + Q_Sand_II = 0.007 m³/s + 0.0022 m³/s = 0.0092 m³/s