It depends on several factors, however, in the best conditions: 1kg cow dung produces 250g of biogas (methane gas) over 24hrs. (55-65% from the gas is metane, CH4).
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You can get about 250 normal litres per kg volatile solids. VS is about 18% of wet fresh manure.
It takes a long time to get that much. The digestion in a batch reactor follows a simple exponential rate law. You can find rate constants in the literature. Just looking at Aslanzadeh's paper I guess something like this:
G = 250 (1 - exp (-0.1 T))
Here G is the number of normal litres CH4 produced after T days from one kg of VS.
It depends on different factors such as the digester type, the biomass feedstock and the temperature etc. please read the publication given in the below link.
As you want to know the required anaerobic time for cow dung, so need to worry about TS, VS variation, and mixture strength, because all these have a certain value for cow dung. Also as you have no choice of temperature in your question, hence consider room temperature. According to Ashrf 1 day is impossible. Perfect time is 7-10 days.