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A water clock consist of a vessel which has a small orifice \( O \). The upper container is filled with water which trickles down into the lower container. The shape of the (upper or lower) container is such that height of water in I lie upper container changes at a uniform rate. Assume that atmospheric air can enter inside the lower container through a hole in it and that the upper container is open at the top. Vessel is axially symmetric. If the relation between radius \( (x) \) of cross-section of water level and the water level height is \( z=\frac{\pi^{2} v_{o}^{2}}{2 g A_{o}^{2}} \cdot x^{k} \). The value of \( k \) is The value of \( k \) is
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