This question was previously asked in

UPPSC AE Civil 2019 Official Paper I (Held on 13 Dec 2020)

Option 1 : a_{v} = constant

**Explanation:**

**Assumptions made in arriving at the Differential Equation for Transient Flow:**

S. No. |
Assumption |
Mathematical Expression |

1 | One dimensional flow in the z-direction |
\({a_v} = constant\) |

2 | Darcy’s Law is valid | \({V_z} = {k_z}\frac{{\partial h}}{{\partial z}}\) |

3 | Soil is homogenous | \({k_z} \ne f\left( z \right)\) |

4 | Flow occurs on account of excess pore water pressure | \(h = \;\frac{u}{{{\gamma _w}}}\) |

5 | Water is incompressible | \({\gamma _w} = constant\) |

6 | The volume of soil solids is constant | \(\frac{1}{{1 + {e_0}}}{d_x}{d_y}{d_z} = constant\) |

7 | Consolidation is occurring under small changes in effective stress | \(\frac{{\partial {v_x}}}{{\partial x}} = \;\frac{{\partial {v_y}}}{{\partial y}} = 0\) |