From the set of equation 4, we conclude that:
i) The ratio of the increase (dH) in BP to the new level H is equivalent to the ratio of the decrease (dQ) in the quantity of blood (Q) required as in equation 4a;
ii) Increase in BP corresponds to a decrease in quantity of blood as shown in equation 4b (Please, note the negative value associated with the parameters on the right hand side of equation);
iii) Increase in quantity of blood, dQ, brings down the BP regime by dH as shown in equation 4c; and
iv) The ratio of the increase, dH, in BP to the decrease in quantity of blood, dQ, is equivalent to the ratio of the BP, H, to the quantity of blood, Q as in equation 4d.
The foregoing equations and conclusions show that mathematically, all the other listed causes of HBP are secondary while the primary cause is shortage of blood. In other words, a patient suffering from HBP should take more blood tonic, blood capsule, blood booster or blood transfusion to boost the quantity of blood. The converse is also true of those suffering from hypotension (low blood pressure).
It should be noted that equation (1a) can be re-written as:
H = (P/ρg)/Q ………………………………………………….(5a)
Or: H = K/Q ………………………………………………………….(5b)
Where: K = P/ρg = constant. Of course, it can still be further inferred that H is inversely proportional to Q and that as Q reduces H increases. But the fundamental mathematical relationship in sets of equation 4 will be obscured and thus excluded.
The adequacy of the conclusions based on sets of equation 4 come from two sources. First, I have used the equations to solve major pipelines troubles to get water delivered from (i) Owena Augmentation Scheme Headworks to Akure, Ondo State in 1991, (ii) Ogunpa lake to University College Hospital (UCH), Ibadan intake station located on a higher ground within the hospital in 2000, and (iii) intake station to all three reservoirs of Middle Ogun Irrigation Scheme, Iseyin, Oyo State in 2004. All these schemes were successfully completed, commissioned after initial hick-ups and still in use.
Perhaps brief information on each project can throw some light on the adequacy of the said governing equation before ending this write up. When Owena Augmentation Scheme was commissioned by the then Military Governor of old Ondo State in 1990, water pumped from Owena Headworks did not reach Olokuta Booster Station from where water was to be pumped to Akure. The pipeline failed the night just before the commissioning. The Governor gave the Management of the Ondo State Water Corporation two weeks to rectify the anomaly or else heads would roll. What caused the failure? Some members of Management thought that a small hill near the Aponmun River caused the problem as it was believed that it hindered the flow.
The solution was to realign the pipeline either through excavation deep into the hill or circumvent it. But someone disagreed with Management. He had another approach. During investigation, he discovered that the installed pumpsets had head H = 109m with a corresponding discharge Q = 490m3/hr. The static elevation difference between Owena Headworks and Olokuta Booster Station Z = 103m. A minimum pressure of P/w = 6m was required at Olokuta Booster Station to ensure that water enters the ground level reservoir.
Velocity head loss during transmission V^2/(2g) = 17m approx. The total head required to drive the flow H1 = 103 + 6 + 17 = 126m. Since the available head H = 109m of the pump was lower than the required head H1 = 126m, the discharge was reduced correspondingly. At a reduced flow Q = 420m3/hr, the operating head of pump increased and water was delivered to Olokuta within 12 days thus meeting up with the deadline given by the Governor. All the efforts made at excavating deep into the hill and realigning the pipeline became a waste because the flow had passed the hill using mere changes in flow.
At the Middle Ogun Irrigation Porject, Iseyin, Oyo State, the headworks had five pumps operating simultaneously with the connected pipeline discharging into three reservoirs (R1, R2 & R5) located at various distances and elevations Z1 = 40m, Z2 = 40m & Z3 = 42m in three sites. Each installed pumpset had head H = 77m with a corresponding discharge Q = 750L/s. The whole process was similar to that of Owena Headworks except that the number of reservoirs increased to three in this instance. For about three years that testing was carried out, it failed each time. In 2003, UTC Water and Power Engineering Ltd were contacted for assistance. During investigation, it was noted that the pipeline size was inadequate to accommodate flows from the five pumps at a time.
Only two of the installed pumps could be operated simultaneously to deliver water to all three reservoirs at the installed capacity. But if flow could be reduced from 750L/s to 600L/s for each pump, three pumpsets could function simultaneously. This approach was adopted and water reached all three reservoirs (For further details, see: Project Review Report, Middle Ogun Irrigation Project, Iseyin, UTC Water & Power Engineering, Apapa, 2003, unpublished). The project was later commissioned by Mr. Olusegun Obasanjo, then President of the Federal Republic of Nigeria. Again, the concept that discharge or flow was inversely proportional to the operating head had been proved right.
At UCH, we transferred the intake station from Ogunpa Lake to the hillside within the hospital to mitigate pilferage by burglars and thieves in 2000. The intake pumps had been delivered to site and intake work started by the Contractor, UTC Water and Power Engineering, when the problem was noticed in 1999. While working in conjunction with the pump manufacturer, Weir Pumps Ltd, Glasgow, we were able to achieve this feat based on the use of equation 1. To the pump manufacturer, it was the first of its kind in the world then. Some other pump manufacturers refused to honour our request for assistance, perhaps the problem was seen as impossible. It is noteworthy that the UCH Water Supply Scheme was commissioned in 2004 by Mr. Olusegun Obasanjo, the President of the Federal Republic of Nigeria.
Second, I suffered from HBP in 2009 and it extended till 2011. Sleep was inadequate while I felt dizzy while walking. I was placed on drugs by the various medical doctors including specialists I consulted. One doctor even advised that I took to regular exercise, a very difficult and near impossible task for me at the time (For further details, see: Omotayo J. A. – One With God, www.ngex.com, Aug 7, 2009).
Later, I had to try traditional herbs. Yet the result was not encouraging. But I had to change to the use of blood capsule by chance, and the result has been wonderful. A marketer introduced a blood capsule to me and I bought it out of pity for the boy whom I learnt was a polytechnic self-trained student. The dizziness and insomnia gradually reduced. The more I used the capsule, the better my condition. Ultimately, I took the locally made Jehovah Witness blood booster from Akure, Ondo State. The dizziness was gone and I slept normally. Today, I take blood booster each time I feel tired and I cannot remember when last I took even paracetamol tablets.
As usual, I welcome criticism(s) and comment(s) either publicly or privately or both. Those criticizing must arm themselves with facts lest they become targets for another critical review. My email address remains: jaomotayo2(at) yahoo.co.uk and my phone 08023235563. CONCLUDED.
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