**Experiment:** To find the time required to empty a burette, filled with water, to ½ of its volume, to ¼ of its volume, to 1/8 of its volume and so on. Then plot a graph between volume of water in the burette and time and thus study at each stage that the fractional rate of flow is same (analogy to radio-active decay).

When a radio-active substance decays, the rate of radio-active decay (measured by intensity of radio-active radiation) decreases by same factor after equal intervals of time. The amount of undecayed substance left also decreases by the same factor after same intervals of time.

The fractional rate of decay = rate of decay of the substance at any instant / amount of undecayed substance left at that instant

The fractional rate of decay remains constant with time.

In like manner, let water flow out through the narrow end of a burette to a thistle funnel and then to a sink. Then the rate of flow of water is proportional to level difference h between the thistle .funnel and water level in the burette at any time, and hence to volume of water in the burette above the bottom mark. Thus,

The fractional rate of flow = rate of flow water / volume of water in burette above the bottom mark

The fractional rate of flow remains constant with time.

**Material Required**

A 50 mL burette with a least count of 0.2 mL or 0.1 mL, a thistle funnel, rubber tube, two laboratory stands, stop clock

Fix the thistle funnel in one stand and the burette in the other. Connect their lower ends by rubber tube. Position the thistle funnel at a place where water overflowing from it falls in a sink, or a wide mouth vessel placed below it. Adjust the heights of the two stands, such that open mouth of thistle funnel is in level with bottom mark of the burette. This may be checked by filling some water in the burette, opening its stopper fully and then noting that water stops flowing out when water level in burette reaches the bottom mark.

This ensures that only pressure of water column in the burette above this marl,, causes the flow of water during the experiment. Put a cotton thread across the diameter of thistle funnel. This helps water to overflow with small level difference too, which may be stopped by surface tension of water.

**1.** After setting up the apparatus, you already have water in the burette upto the bottom mark and in the thistle funnel. Close the stopper and fill water in the burette upto a little above its upper mark.

**2.** Gently open the stopper a little so that water starts flowing slowly. At the same time start the stop watch. Water flow should be rather slow so that water flowing through narrow opening in the stopper does not become turbulent.

**3.** As the water level reaches the upper mark of the burette, note the time shown in the stop clock, without stopping it.

**4.** At every 5 mL fall of water, level note the time in the stop clock without stopping it. There is an inevitable time lag between observing water level reach a certain mark on the burette and then observing the time shown in the clock at that instant. But this time lag can be maintained approximately constant with some practice.

During these observations the stopper of the burette should not at all be disturbed. If you feel that water flow is much too slow or fast and there ispneed to alter it, then you have to start from step (1) again. The resistance to water flow by stopper must not be changed during these observations.

After water level comes down to a low value, e.g. 20 mL, then rate of flow becomes slow and you may like to note the tirre at every 2 mL fall of water level instead of 5 mL.

**5.** Plot a graph between volume of water in the burette, V (along y-axis), versus observed time, t, in the stop clock (along x-axis).

**6.** From the graph read values of t when V reduces to 40 mL, 20 mL, 10 mL, 5 ml and 2.5 mL. Calculate the time intervals T (1/2), T (1/4), T (1/8), T (1/16) taken to reach last four values from V = 40mL. Calculate half life of water flow in each case, i.e. time taken to reduce V to half values: T (1/2)/1, T (l/4)/2, T (l/8)/3, T (l/16)/4.

**7.** Draw tangents to the graph at each of these five values of v, and find the slopes ΔV/Δt = rate of flow.

**8.** At each of these five values of V, find the fractional rate of flow water:

= rate of flow of water at an instant / volume of water in the burette at that instant

- Time lag between observing a certain value of V in the burette and then observing the corresponding time t in the stop clock, may not be same for all readings.
- If water flow is even slightly turbulent during higher values of V in the beginning, then fractional rate of flow will be too low at that time.