The pendant drop method is frequently used for the study of liquid-liquid interfacial tension. I guess your water phase has a higher density then the used oil.

If this is correct the drop which is generated at the tip should consist of the water phase. The oil is placed in a beaker and the tip of the pending drop machine is placed inside the oil. Then you generate the drop an analyze the shape using the Young-Laplace equation. The important point is that the surfactant concentration in both phases should correspond to the concentration in the emulsion. Hence, you need to know how the stabilizing surfactant is partitioned between the two phases.If you dissolve the surfactant only in the oil phase the drop shape will be influenced by the adsorption kinetics of the surfactant, which has to be taken into account. An interesting work in this context might be the following one:

DOI 10.1016/j.jcis.2016.06.062 by Alexander Boeker. However, this work deals with the Pickering effect and Pickering emulsions.

Thank you Thomas Hellweg sir for your reply. Can you specify which oil is used in the beaker to determine interfacial tension of oil in water emulsion? i would like to mention here that, my sample is a crude oil in water emulsion which is dark in colour as oil % is more (close to inversion point), so i cannot use crude oil in the beaker as the oil phase. Here, only my sample contains surfactant. Are you suggesting that the oil phase used for analysis should also contain same surfactant?