Motor Power Calculator

Are you sure the weight is 20 kg? Not more not less?

What would be the flow rate?

What food?

Is the conveyor measurement OD or ID?

How many screw windings?

In short the answer is you will need an electric motor!

Just follow the directions....
http://www.kwsmfg.com/services/screw-conveyor-engineering-guide/horsepower-calculation.htm

The power of any motor is the shaft torque multiplied by the angular velocity divided by the motor's efficiency:

• The angular velocity is determined by the gearbox ratio between the motor output shaft and the suitable angular velocity of the driven piece of equipment.
• The torque on the motor shaft is a function of the following variables:
• The rate of lift of the 20kg load against a gravitational pull (does one assume Earth's gravity?)
• The friction between the food material and the food driving device
• The efficiency of the gearbox arrangement between the motor shaft and the food driving device
• other factors such as air resistance

about which the forum knows nothing yet.

Are you still in high school?

Is this your project?

Is your screw geared or direct drive?

What is the pitch of the screw conveyor? Or how much food material per minute being processed.

What is the coefficient of friction between the food material and the conveyor wall?

What direction is the food material traveling? Horizontal? Vertical up? Vertical down? Angle?

What is the unloaded power consumption of the gear sets and bearings?

Is the question to find the input power to the motor or the power provided by the motor?

I'll give you a hint: The weight of the screw conveyor is a distractor in this homework question but there isn't enough information in this question to answer this even if we assume friction-free movement. Go back to your teacher/professor for more information.