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题类比水压是形成水流的原因,李楠同学猜想,血液在血管内流动时也需要一定的压力差来维持．假设血液匀速通过长度一定的血管时,受到的阻力f与血液的流速v成正比,即 f=kv．那么,要想让血液匀速流过,血管两端就需要一定的压力差．设血管截面积为S1时, 两端所需的压强差为△p1;若血管截面积减少 10％时,为了维持在相同的时间内流过同样体积的血液,压强差必须变为△p2．请你通过计算比较△p1、△p2的大小,说明血管变细可能是诱发高血压的重要因素之一．
The analogy of water pressure is the cause of water flow. Li Nan’s conjectures that when blood flows in blood vessels, it also requires a certain pressure difference to maintain it. Assuming that the blood flows through a certain length of blood vessel at a constant speed, the resistance f received is proportional to the blood flow velocity v, ie, f=kv. Then, in order for the blood to flow at a constant speed, a certain pressure difference is required at both ends of the blood vessel. When the blood vessel cross-sectional area is S1, the required pressure difference at both ends is Δp1; if the blood vessel cross-sectional area is reduced by 10%, in order to maintain the same volume of blood flowing in the same time, the pressure difference must be changed to Δp2. Please calculate by comparing the size of △p1, △p2, indicating that blood vessel thinning may be one of the important factors inducing hypertension.