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The area-equivalent lumen diameter is the diameter of a circle having the same area as a measured lumen. For positive area $A$,It converts an area observation into a length scale without asserting that the actual lumen is circular. The definition applies to an irregular outline as well as to an ideal geometric shape.

For an ellipse with full principal diameters $D_1,D_2$, area is $A=\pi D_1{D}_2/4$, soAn original ellipse with diameters $4$ and $2\mathrm{mm}$ has area $2\pi \mathrm{m}{\mathrm{m}}^2$ and area-equivalent diameter $2\sqrt{2}\simeq 2.828\mathrm{mm}$. The arithmetic mean of its two diameters is $3\mathrm{mm}$, which would define a circle of larger area.

Using an equivalent diameter in a circular area-ratio formula is valid by construction:Using an arbitrary single projected width instead is not. Eccentric lumen stenosis can show different widths in different views while retaining the same area. Primary selective coronary arteriography used serial and cine recording to observe the contrast-filled arterial route; interpreting such images still requires the chosen projection and reconstruction model.^[ref]

The equivalent diameter also differs from hydraulic diameter, $D_h=4A/P_w$, which includes wetted perimeter $P_w$. Two equal-area outlines can have different perimeters and flow resistance. An area-equivalent circle is therefore not automatically an equivalent flow model.

For small area uncertainty, differentiation gives $\mathrm{d}{D}_A/D_A=\frac{1}{2}\mathrm{d}A/A$. A $4\%$ relative standard uncertainty in area gives approximately $2\%$ in the derived diameter if other inputs are fixed. This propagates area uncertainty; it does not correct an incorrectly segmented outline or a mismatched reference region.

Continue the same-rod-number and same-height comparison from part(a), and assume unchanged pump speed, similar inlet conditions and single-phase forced flow for the normal-operation hydraulic argument.

Core power density increases. The active core volume decreases while total thermal power stays fixed. The fuel's own average volumetric power and the mean fuel linear heat rate do not increase merely from bringing the same rods closer together: fuel volume and rod count are unchanged.

Coolant mass flow rate normally decreases. Tighter passages reduce flow area and hydraulic diameter, increasing the core's hydraulic resistance. The unchanged centrifugal pumps do not enforce constant flow. The pump operating point moves to the intersection of the same pump curve with the steeper system-resistance curve, normally giving smaller flow at greater pump head.^[ref]

The core pressure drop normally increases for the usual pump curve. Its resistance at any given flow is higher. At the new, smaller flow, unchanged external piping and component losses are smaller, whereas a conventional falling pump head-versus-flow curve gives greater available head. The core takes the difference. This conclusion uses the stated pump-curve assumptions; holding flow fixed or holding pump head fixed would be different models. The exact new flow and pressure drop need both system and pump characteristics.

Fuel temperature would normally tend to rise, especially downstream, if the loss of flow increases coolant heating without a compensating improvement in film heat transfer. At fixed inlet state,shows that smaller total mass flow rate raises the bulk coolant temperature rise. At unchanged local fuel linear heat rate, the fuel-to-surface conductive contribution is approximately unchanged if material properties and gap conditions are held fixed. Its boundary temperature and the coolant film drop can nevertheless change.

The local coolant mass flux is $G=\dot{m}/A_f$. Both total flow and flow area decrease, so the sign of the change in $G$, the heat transfer coefficient and the fuel temperature cannot be deduced from total flow alone. Changes in power peaking and inlet conditions add further qualifications to the usual hotter-fuel tendency.

The minimum departure from nucleate boiling ratio would commonly decrease, implying reduced boiling margin, but its sign is conditional. The defining local ratio isThe numerator is the critical heat flux for the local conditions, and the denominator is actual rod-surface heat flux.^[ref] The mean surface heat loading remains approximately unchanged for the same rods and total power. Greater coolant enthalpy rise tends to reduce margin, while changes in $G$, geometry, pressure and local power determine the actual critical heat flux. A geometry-appropriate correlation or experiment is needed for a definite MDNBR change; unchanged hardware does not supply it.