In V band, extinction is about 0.1 mag/airmass.
The Sun's apparent brightness is -26.74.
0.1 mag of extinction means that about 10% of the light is taken from the sun and spread over the sky, about 21,000 square degrees. Half of this is scattered out of the atmosphere, half down to make the blue sky.
The integrated magnitude of the sky would then be of order -26.74 + 2.5*log10(10*2) = -23.5.. i.e. 3.2 magnitudes dimmer than the Sun.
Spreading this over half the sky (21000 square degrees or 2.7E11 square arcseconds) gives a reduction in surface brightness by 2.5*log10(2.7E11) = 28.6 magnitudes.
This yields a daytime sky brightness in V band of -24.24+28.6 = 4 mag square arcsecond.
If we have any daytime exposures with the ES telescope -- we could check this and get numbers in other bands as well...