Thank you for your question to "Ask Extension".
With drip irrigation, water moves downward and sideways, creating a balloon-shaped wetted zone. The shape and depth depend heavily on soil texture, organic matter, compaction, slope, and how long you run the system—so the surface can look dry even when the root zone is wet.
Because you can’t judge the wetted “balloon” by looking at the soil surface, using a timer and doing a little on-site checking (dig/probe) is strongly recommended.

     A reasonable starting-point math approach is:
     It takes 0.62 gallons per square foot to apply 1 inch of water.

So if you can estimate the area being effectively wetted (in sq ft), you can estimate runtime.

If one emitter effectively wets about 2 sq ft of clay soil, then:

Water needed for 1 inch over 2 sq ft = 0.62 × 2 = 1.24 gallons
With a 0.5 GPH emitter, time to apply 1.24 gal = 1.24 ÷ 0.5 = ~2.5 hours.

The best practical way to answer this for your bed (quick test).
   Run your drip zone for the time you’re considering (e.g., 60–120 minutes).
   Wait ~30–60 minutes (so water redistributes a bit in the soil).
   Dig a small hole or use a soil probe a few inches away from an emitter and check how deep the soil is moist.
This is the most dependable way to calibrate your runtime to your soil and layout, especially in “clayish” soils. The “surface looks dry” issue is common with drip.
     
A broad landscape rule-of-thumb is to adjust irrigation so that rain + irrigation totals about ~1 inch per week during the growing season, then modify based on plant response and site conditions. 

• Start with 1–2 irrigations per week, and make each one “long enough” to reach the active root zone (your dig/probe test tells you what runtime does that on your site).
• Then adjust up/down based on heat, exposure, plant stress, and how quickly the bed dries. (ET rises as temperatures rise.)

     I hope that you find this information helpful and as always Happy Gardening.

Thank you so much for your clear & thorough answer! It has given me a much better understanding & overview of how to apply the drip system at my location.