Beets should be evenly moist. Not enough water and they become dry and woody, sort of stringy inside. They also prefer a loose rich soil. Beets are also what I call cool weather plants. They like a sunny location but not a real hot location. They can take a couple of degrees of frost as well. I prefer the varieties that are cylindra...in other words they grow like a carrot. I also grow golden beets but they are prone to getting a bit of scab.
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Best way to figure out if any plant needs water is to dig down a bit with your fingers. Beets should be evenly moist down to 2 or 3 inches, depending on their size and when you planted them.
I have found that once cucumbers get powdery mildew, there is not much you can do except stop watering for awhile. Don't water cucumbers in the evening, especially in Calgary where our evenings cool off. Evening watering plus cool evenings spell mildew for cucumbers.
Cucumbers are a hot weather plant. Plant them in your hottest and sunniest spot and where water does not pool. I only water mine in the morning. When cucumbers start to produce, they will need more water as the fruit can tend to dry out with insufficient watering.