An apparatus for processing molten glass comprising: a forming body comprising a trough positioned in a top of the forming body; a delivery vessel comprising a delivery vessel outlet conduit, the delivery vessel configured to supply molten glass to the forming body trough through a delivery conduit configured to deliver the flow of molten glass to the forming body trough, the delivery conduit comprising: a first portion having a straight longitudinal axis and a circular cross section, wherein at least a portion of the delivery vessel outlet conduit extends within but does not contact at least a length of the first portion, there being an annular gap separating the at least a portion of the delivery vessel outlet conduit from the first portion of the delivery conduit; a second portion configured to direct the flow of molten glass from a first direction to a second direction different from the first direction; a third portion having a straight longitudinal axis, and an inside bottom surface; and a first transition portion that connects the second portion to the third portion, wherein the third portion has a non-circular cross-section comprising sidewalls (102a, 102b) and planar top and bottom walls (104a, 104b), wherein a maximum inside height H between midpoints of the planar top and bottom walls (104a, 104b) is less than a maximum inside with W between mid-points of the side walls (102a, 102b); in that the delivery conduit further comprises a second transition portion that couples the third portion to the forming body trough, the second transition portion having an inside bottom surface; and in that the bottom surfaces (106, 114) of the third portion and the second transition portion are no lower than a bottom surface of the trough. a forming body comprising a trough positioned in a top of the forming body; a delivery vessel comprising a delivery vessel outlet conduit, the delivery vessel configured to supply molten glass to the forming body trough through a delivery conduit configured to deliver the flow of molten glass to the forming body trough, the delivery conduit comprising: a first portion having a straight longitudinal axis and a circular cross section, wherein at least a portion of the delivery vessel outlet conduit extends within but does not contact at least a length of the first portion, there being an annular gap separating the at least a portion of the delivery vessel outlet conduit from the first portion of the delivery conduit; a second portion configured to direct the flow of molten glass from a first direction to a second direction different from the first direction; a third portion having a straight longitudinal axis, and an inside bottom surface; and a first transition portion that connects the second portion to the third portion, wherein the third portion has a non-circular cross-section comprising sidewalls (102a, 102b) and planar top and bottom walls (104a, 104b), wherein a maximum inside height H between midpoints of the planar top and bottom walls (104a, 104b) is less than a maximum inside with W between mid-points of the side walls (102a, 102b); in that the delivery conduit further comprises a second transition portion that couples the third portion to the forming body trough, the second transition portion having an inside bottom surface; and in that the bottom surfaces (106, 114) of the third portion and the second transition portion are no lower than a bottom surface of the trough. a first portion having a straight longitudinal axis and a circular cross section, wherein at least a portion of the delivery vessel outlet conduit extends within but does not contact at least a length of the first portion, there being an annular gap separating the at least a portion of the delivery vessel outlet conduit from the first portion of the delivery conduit; a second portion configured to direct the flow of molten glass from a first direction to a second direction different from the first direction; a third portion having a straight longitudinal axis, and an inside bottom surface; and a first transition portion that connects the second portion to the third portion, wherein the third portion has a non-circular cross-section comprising sidewalls (102a, 102b) and planar top and bottom walls (104a, 104b), wherein a maximum inside height H between midpoints of the planar top and bottom walls (104a, 104b) is less than a maximum inside with W between mid-points of the side walls (102a, 102b); in that the delivery conduit further comprises a second transition portion that couples the third portion to the forming body trough, the second transition portion having an inside bottom surface; and in that the bottom surfaces (106, 114) of the third portion and the second transition portion are no lower than a bottom surface of the trough.