Blood Flow, Resistance and Pressure

Equation 1: Mean Arterial Blood Pressure = Cardiac Output X Total Peripheral Resistance
Equation 2: Blood Flow = Δ Blood Pressure* / Peripheral Resistance#
*, between the ends of a blood vessel
#, along a blood vessel

If you increase the diameter of a blood vessel then you decrease the resistance to blood flow
along that blood vessel. If the difference in blood pressure between the beginning and the end of
this blood vessel does not change, then according to equation 2, blood flow should increase.
But, equation 1 suggests that if you decrease resistance then you should decrease blood pressure.

According to equation 2, if you decrease blood pressure then blood flow should decrease.
Therefore, there appears to be a conflict between the two equations with a decrease in resistance
(equation 2) leading to an increase in blood flow but also leading to a decrease in blood pressure
(equation 1) which should, in turn, lead to a decrease in blood flow (equation 2). However, there
is no conflict.

Think carefully about what the two equations represent and indicate why this
apparent conflict does not exist.