Does lift equal weight in level flight? Or does it equal weight + down pressure on the tail?
Added) Let's say the total weight of the aircraft on the ground was 100,000 lbs, and when it took off and leveled off, the down force from the tail was 10,000 lbs. Then what's the total lift required to support the level flight?
When you consider the aircraft as a whole, lift equals weight in level flight. This must be true following the laws of physics.
However, if you break down the forces, the lift produced by the wings does not necessary equal to the weight of the aircraft. Lift is also generated by the body (albeit very inefficient) and by the tail. Most horizontal stabilizers generate negative lift, but some (e.g. the A380) generate positive lift.
If we ignore the fact that fuselage produces lift, and assume a configuration where the tail produces downward force, then you are correct. But the fuselage does produces lift. Modern aircraft designs use software to take that into account.
What exactly you mean by "lift" is important to answer this question. In unaccelerated flight (steady speed, constant rate of climb or descent, including level flight), all forces on the airplane are balanced - forward equals backward, up equals down, and left equals right. Weight is generally a downward force, lift upward, drag backward, thrust forward, and sideways force is generally minimal, but comes from things like rudder trim or the various forces involved in P-Factor (this also changes based on how you define "up", as in a turn lift will become a partially sideways force if "up" is defined by something outside the airplane, e.g. earth).
If by lift you mean the sum of all up/down aerodynamic forces (which is how I tend to think of it, in general, though this is not technically correct - see footnote or linked article) and by "up" you mean "directly away from earth's center of gravity", then yes, lift equals the aircraft's weight in unaccelerated flight. There may be some negative lift (as you say in your example, the 10,000 pounds of tail-down force), but this will be balanced by additional upward lift over the airplane's weight - that is, if the sum of all downward aerodynamic forces is 10,000 pounds and the aircraft weighs 100,000 pounds, then the sum of all upward aerodynamic forces must be 110,000 pounds. However, when speaking of the sum of forces, we must remember to treat them like the vectors they are - so 110,000 pounds of upward lift plus 10,000 pounds of downward lift equals 100,000 pounds of net upward lift - the airplane's weight.
If your definition of lift does not include that created by the engines (i.e., "vertical component of thrust"), or really, if you use any other definition without restricting it to special cases, then this may or may not be true - if the vertical component is zero (it's usually small, but probably not quite zero), then total lift will equal aircraft weight for unaccelerated flight. If it is nonzero, then lift plus the vertical component of thrust will equal weight, but lift alone will not equal weight in unaccelerated flight.
Footnote on the definition of "lift": the technical definition of the lift force is the component of force exerted on a body by fluid flowing past it which is perpendicular to the flow of the fluid - so my definition would include the drag of a falling body as a "lift" force, which it is not.
Short Answer: No
Long Answer:
In real flight the equilibrium of forces in the Z axis is a little bit more complex. You should consider also the effect of the different angles and component of Thrust as indicates the next Figure:
The equation should be:
If we consider static flight without normal acceleration and considering small values for the angles; the Lift Force would be $L = W-T*alpha$
Yes. Lift equals weight in level flight.
A better way to say would be that in case of a steady level flight, the aerodynamic forces (including the propulsive force) and the body force are in equilibrium.
The aerodynamic force includes the lift created by the wing, fuselage, the down force created by stabilizer etc. So, in your case, the lift equals the weight plus the tail down-force.
You also forgot thrust. Particularly with vectored thrust at slow speed, you can get level flight with a high angle of attack/thrust vector and most of the weight is counteracted by thrust. e.g. this harrier transitioning to level flight
or this park flyer struggling into a head wind at an almost vertical angle of attack (hence little aerodynamic lift) . Both of these are flying level with near to zero aerodynamic lift.Net lift can be considered to be acting at 90 degrees to the velocity. Net lift includes contributions from wings, tail, canards, brakes, flaps and body, some of which may be acting upwards or downwards. Weight acts downwards. Thrust can acts at an angle to the velocity, either due to pitch or vectoring. So depending on pitch or vectoring, even if velocity is horizontal and net lift vertical, thrust can have a vertical component which acts against some of the weight.
