This paper presents a measurement of the charged current interaction rate of the electron neutrino beam component of the beam above $1.5$~GeV using the large fiducial mass of the T2K $pi^0$ detector. The predominant poriton of the $ u_e$ flux ($sim$85 %) at these energies comes from kaon decays. The measured ratio of the observed beam interaction rate to the predicted rate in the detector with water targets filled is 0.89 $pm$ 0.08 (stat.) $pm$ 0.11 (sys.), and with the water targets emptied is 0.90 $pm$ 0.09 (stat.) $pm$ 0.13 (sys.). The ratio obtained for the interactions on water only from an event subtraction method is 0.87 $pm$ 0.33 (stat.) $pm$ 0.21 (sys.). This is the first measurement of the interaction rate of electron neutrinos on water, which is particularly of interest to experiments with water Cherenkov detectors.
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