M3Q11

The river channel of an estuary is 350 m wide and 5 m deep. Assuming a tidal range of 0.8m and average tidal current speed of 0.15m/s, how far upriver would the tide go? (Answer in km)

Question

M3Q11

The river channel of an estuary is 350 m wide and 5 m deep. Assuming a tidal range of 0.8m and average tidal current speed of 0.15m/s, how far upriver would the tide go? (Answer in km)

BlackTom AI · Accepted Answer

To estimate how far upriver the tide would propagate, we can treat the tide as a shallow-water wave propagating through the estuary. The speed of a shallow-water wave is given by c = sqrt(g h), where g is gravitational acceleration and h is the water depth.

First, compute the wave speed with the given depth: h = 5 m and g ≈ 9.81 m/s^2.
c = sqrt(9.81 × 5) ≈ sqrt(49.05) ≈ 7.0 m/s.

Next, we need the time scale over which the tide travels upriver. A semidiurnal tide has two cycles per day, so the flood/ebb half-cycle lasts about half a tidal period. The typical half-period is roughly 6.2 hours, which is about 6.2 × 3600 ≈ 22,300 seconds.

Now multiply wave speed by this time to get the distance the tidal front can travel:
Distance ≈ c × time ≈ 7.0 m/s × 22,300 s ≈ 156,100 m.
Convert to kilometers: 156,100 m ≈ 156 km.

Therefore, the tide would travel roughly on the order of about 156 km upriver under these assumptions. If you round to the nearest whole kilometer, you get approximately 156 km.

CVEN90051_2024_SM2 Mock Exam 2024

M3Q11 The river channel of an estuary is 350 m wide and 5 m deep. Assuming a tidal range of 0.8m and average tidal current speed of 0.15m/s, how far upriver would the tide go? (Answer in km)

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M3Q11 PART#1 The river channel of an estuary is 350 m wide and 5 m deep. PART #1: Assuming a tidal range of 0.8m and average tidal current speed of 0.15m/s, how far upriver would the tide go? (Answer in km).

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