Water flow water is not pumping through engine

You may have gotten the wrong pump. Some are reverse rotation, depending on your belt routing. Remove the thermostat and see if the coolant is flowing in the PROPER direction.

cool engine . open radiator water cap, run engine till hot it will click an you will see water flow in radiator , no click then thermostat is bad ,, click but no flow pump is stopped up dead bad

Looks like the pump has failed; most times caused by freeze damage. If you store over the winter, you need anti-freeze in pump.

Yes. It could be th water pump.

The first thing you need to check is if you have the water supply hocked to the mechine with no pressure line connected just the water dose it spray out the pressure line connecter with out the engine running . If this dosen't happen the water pump is no good . You can never start any kind of mechine like this with out constant water flow . It sounds like something is broken between the engine shaft and the pump the pump is likely seized and this broke the connection between the engine and the pump. If this is the case the mechine is likely not worth the money you would have to put into it to save it

The hose from the radiator to the water pump is flowing into the engine.

coolong system flows from the top of the engine to the top rad, flows down out the bottom to the water pump then through the engine, sounds like the thermostat is frozen solid,

When the engine has cooled down check the coolant level and make sure it is full. Are you sure you temperature gauge is accurate? If the coolant is in the operating range, I would suspect one of two problems, water pump or thermostat. With the engine on check to make sure the serpentine belt (should be only one belt for your engine) is turning the pulley for your water pump is rotating without restriction. The thermostat will allow coolant flow when it reaches operating temperate. You may be able to squeeze the hose and feel the pressure of the water flow when the engine is heating up. If you have no flow check the thermostat first and if the flow of coolant is not circulating when the engine warms up you will have to drain the coolant to remove the pump to check the operation and replace if necessary.

you probably have air trapped in the system. Have dealer or radiator shop bleed system.

I assume your cooling fan is working.

what engine v6 or v8?

SECTION 303-03: Engine Cooling 2001 Lincoln LS Workshop Manual
DESCRIPTION AND OPERATION Engine Cooling The cooling system components include the:

• block heater (optional)
• cylinder head temperature sensor
• fan blade, fan motor and fan shroud assembly
• radiator
• pressure relief cap
• degas bottle
• radiator draincock
• water pump
• oil cooler (optional)
• water thermostat

The water thermostat:

• controls the engine coolant temperature.
• allows quicker engine warm-up.

The degas bottle:

• provides a location for system fill.
• contains coolant expansion and system pressurization.
• provides air separation during operation.
• replenishes the engine coolant to the system.

The fan blade draws air through the radiator to help cool the engine coolant.
The fan motor:

• operates only when the engine is running.
• will not operate when the engine is off.

The engine coolant flows:

• from the lower radiator hose to the water pump.
• from the water pump to the engine block and the cylinder heads.

A closed water thermostat returns the engine coolant to the water pump. An open water thermostat allows the engine coolant to flow to the radiator.
Unsatisfactory coolant materials:

• Alcohol-type antifreeze does not provide adequate water pump lubrication.
  • has lower boiling point
  • reduced antifreeze protection
• Alkaline brine solutions will cause serious engine cooling system damage.

The cylinder head temperature sensor provides a signal to the temperature gauge.

• will invoke failsafe cooling.

The optional block heater:

• electrical heating element is installed in the block cooling jacket.
  • uses a standard 110V (220V in Europe) electrical supply
• keeps the engine coolant warm during cold weather.

The auxiliary water pump (3.9L only):

• provides heater coolant flow boost.
• has a secondary function of providing engine-off cooling.

You need either a new thermostat or a new water pump.