Blood flows from Point A to Point B at an initial velocity of 100 cm/s within an artery supplying the brain. Assume negligible blood pressure change as the blood ascends 1 cm in the head. What is the velocity of blood flow when the blood reaches Point B? (Note: The density of blood is 1,060 kg/m³.)

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11ecba2d_130b_6022_a3bf_19950df2b87f_MD0008_00 The total energy contained within a volume of fluid remains constant as it flows from one point to another within a conduit, following the law of conservation of energy. As a result, the total energy at any two points along the path of fluid flow must be equal: 11ecba2d_130b_6023_a3bf_c57ec2301351_MD0008_00 Total EnergyPoint A=Total EnergyPoint B Like solid objects, fluids possess both kinetic energy and potential energy between two points. The difference is that fluid kinetic and potential energy are both related to fluid density (ρ) rather than mass: 11ecba2d_130b_6024_a3bf_a5c596044cd5_MD0008_00 ρghA+12ρvA2=ρghB+12ρvB2 Pressure (P) is also relevant to energy conservation in fluids because it may be expressed as a measurement of energy per unit volume. Adding terms for the energy contributions from pressure yields Bernoulli's equation, a mathematical expression for the conservation of potential energy, kinetic energy, and pressure energy of a fluid traveling through a conduit: 11ecba2d_130b_6025_a3bf_edf726aab0f0_MD0008_00 PA+ ρghA+12ρvA2=PB+ρghB+12ρvB2 In this question, blood travels at an initial velocity (v_A) of 100 cm/s (1 m/s) from Point A to Point B within an artery under constant pressure. Because blood pressure is constant (P_A = P_B), the pressure terms can be eliminated from Bernoulli's equation, which can be rearranged to solve for the unknown velocity (v_B): 11ecba2d_130b_6026_a3bf_b9168876b212_MD0008_00 11ecba2d_130b_8737_a3bf_95fef8cdd277_MD0008_00 11ecba2d_130b_8738_a3bf_af6ea4ada496_MD0008_00 The distance the fluid traverses vertically (h_B − h_A) is 1 cm (0.01 m). Substituting this value and the initial velocity into the above equation yields: 11ecba2d_130b_8739_a3bf_6f74d3f637f7_MD0008_00 11ecba2d_130b_873a_a3bf_cbdf6d021f19_MD0008_00 11ecba2d_130b_873b_a3bf_9d526c5e104a_MD0008_00 Therefore, the velocity of blood that ascends 1 cm in the neck decreases from 100 cm/s to 90 cm/s when it reaches Point B. Educational objective: Fluid flows in accordance with the conservation of energy. Bernoulli's equation can be used to determine the total potential, kinetic, and pressure energy of a fluid at two points within a conduit.

Blood Flows from Point a to Point B at an Initial