1. Stream order of Logan River at its mouth
The stream order of the Beaver Creek is 4. Similarly the stream order of the Temple Fork is also 4. At the confluence with Beaver Creek, stream order of Logan River becomes 4. Similarly, on travelling further downstream, Temple Fork with a stream order of 4 joins the Logan River. So, after that the stream order of Logan River becomes 5. From the confluence with Beaver Creek to the confluence with Temple Fork, stream order of 4 is maintained as there are no streams of higher or same order joining the Logan River in between. Similarly, after attaining a stream order of 5, no streams of higher or same order joins the Logan. Hence the stream order of Logan River at its mouth is 5.
2. Stream order of Temple Fork at its mouth
The Logan River at its mouth has a stream order of 4. Please refer the above figure on the top left.
3. Stream order of Beaver Creek
The Beaver Creek has a stream order of 4. Please refer the above figure on the top right.
4. Does Logan River appear to obey Hortonian laws of stream network composition ?
The three Hortonian laws and adherence of Logan River to those laws are explained as follows:
Law 1: As stream order increases number of streams of a given order decrease
If we refer to the drainage network of the Logan River we can observe that there are many drainage lines of order 1. Only a few streams have order of 4. So, there are more streams of order 1 than there are streams of order 4. Clearly, with the increasing stream order, streams with that order are decreasing. Hence, the Logan River obeys Law 1.
Law 2: As stream order increases mean stream length increase
Before joining the Beaver Creek (stream order 3), the stream order of Logan River is 3. But, after joining the Beaver Creek its stream order becomes 4. After going further downstream, it joins Temple Fork which has a stream order of 4. Hence, after the confluence, the stream order of Logan River becomes 5. So, we can say that Logan River follows law 2.
(Although its possible that the stream order might not increase even though the mean stream length increases. But, the law itself does not mention about the inverse)
Law 3: As stream order increases catchment area increase
The stream order of the Logan River becomes 4 from 3 after the confluence with Beaver Creek and gains the catchment area of that creek. Similarly, it gains the catchment area of Temple Fork after joining it and the stream order also increases to 5 from 4. Hence, the catchment area of the Logan River shows an increasing trend with increasing stream order. It's safe to say that the Logan River obeys the third law also.