Question

I.C. At the right is shown a pipe with a uniform circular cross-section carrying fluid at a steady flow. The piece of the pipe we are considering has a length, L, and a cross-sectional area, A. The fluid is flowing at a rate of Q. Flow has dimensionality of volume per second ({Q} = L^3/T). The pressure at the beginning of the segment is p1, and at the end of the segment is p2, with ?p = p1 - p2. Pressure is force per unit area, so it has dimensionality {p} = M/LT^2 (= {F/A} = (ML/T^2) / L^2). The fluid has a viscosity, ?, which has dimensionality {?} = M/LT. In thinking about the flow of blood in an artery, we are interested in how the flow we get is changed as the parameters of the situation change. Let's rewrite the H-P equation that tells the flow produced by a pressure drop. Some equations giving the flow, Q, resulting from a pressure difference, ?p, are shown in the table below. Some have incorrect dimensions and therefore have to be wrong. Some have implausible functional dependence on a parameter and therefore have to be

          I.C.
At the right is shown a pipe with a uniform
circular cross-section carrying fluid at a steady
flow. The piece of the pipe we are considering
has a length, L, and a cross-sectional area, A.
The fluid is flowing at a rate of Q. Flow has
dimensionality of volume per second ({Q} = L^3/T).
The pressure at the beginning of the segment is p1, and at the end of the
segment is p2, with ?p = p1 - p2. Pressure is force per unit area, so it has
dimensionality {p} = M/LT^2 (= {F/A} = (ML/T^2) / L^2).
The fluid has a viscosity, ?, which has dimensionality {?} = M/LT.
In thinking about the flow of blood in an artery, we are interested in how the
flow
we get is changed as the parameters of the situation change. Let's rewrite
the H-P equation that tells the flow produced by a pressure drop.
Some equations giving the flow, Q, resulting from a pressure difference, ?p,
are shown in the table below.
Some have incorrect dimensions and therefore have to be wrong. Some have
implausible functional dependence on a parameter and therefore have to be

I.C.
At the right is shown a pipe with a uniform
circular cross-section carrying fluid at a steady
flow. The piece of the pipe we are considering
has a length, L, and a cross-sectional area, A.
The fluid is flowing at a rate of Q. Flow has
dimensionality of volume per second (Q = L^3/T).
The pressure at the beginning of the segment is p1, and at the end of the
segment is p2, with ?p = p1 - p2. Pressure is force per unit area, so it has
dimensionality p = M/LT^2 (= F/A = (ML/T^2) / L^2).
The fluid has a viscosity, ?, which has dimensionality ? = M/LT.
In thinking about the flow of blood in an artery, we are interested in how the
flow
we get is changed as the parameters of the situation change. Let's rewrite
the H-P equation that tells the flow produced by a pressure drop.
Some equations giving the flow, Q, resulting from a pressure difference, ?p,
are shown in the table below.
Some have incorrect dimensions and therefore have to be wrong. Some have
implausible functional dependence on a parameter and therefore have to be

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