(a) Find the transient solution Pran(t) for the arterial pressure. The unit for P(t) is mmHg. (b) Determine the steady-state solution Pss(t) for the arterial pressure. (c) Determine the total solution P(t) assuming that the initial arterial pressure is 0.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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3. The relationship between arterial blood flow and blood pressure in a single artery satisfies the
following first-order differential equation:
dP(t)
+
dt RC
mmHg
(cm³/s)
P(t) =
where Qin is the volumetric blood flow, R is the peripheral resistance, and C is arterial
compliance (all constant). Qin-60 cm³/s and the initial arterial pressure is 6 mmHg.
Also, assume R = 4
and C= 0.4-
Oin
cm³
mmHg
(a) Find the transient solution Ptran(t) for the arterial pressure. The unit for P(t) is mmHg.
(b) Determine the steady-state solution Pss(t) for the arterial pressure.
(c) Determine the total solution P(t) assuming that the initial arterial pressure is 0.
Transcribed Image Text:3. The relationship between arterial blood flow and blood pressure in a single artery satisfies the following first-order differential equation: dP(t) + dt RC mmHg (cm³/s) P(t) = where Qin is the volumetric blood flow, R is the peripheral resistance, and C is arterial compliance (all constant). Qin-60 cm³/s and the initial arterial pressure is 6 mmHg. Also, assume R = 4 and C= 0.4- Oin cm³ mmHg (a) Find the transient solution Ptran(t) for the arterial pressure. The unit for P(t) is mmHg. (b) Determine the steady-state solution Pss(t) for the arterial pressure. (c) Determine the total solution P(t) assuming that the initial arterial pressure is 0.
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