C172 instructor reported engine failure during pattern work with student.

Narrative:

My student and I were doing pattern work; and we had done 6 touch and goes including 2 slips; simulated engine failure by pulling power to idle and a go-around. On our last pattern my student pulled power to 1500 rpm abeam the numbers (runway xx was the runway we were cleared touch and go) the student put in flaps 10 and then turned base. On the base leg I noticed that the RPM indicator showed 1000 rpm so I asked my student why did you pull the power to idle; then I realized the student had not but the engine had failed and in fact the student had given full power and it was still showing 1000 rpm. So I took the controls and noticed the mixture was rich; fuel selector was on both and the fuel shut off value was in. I pitch for best glide and told tower we had an engine failure and asked to land on runway xy. They said I was cleared to land (I chose that runway because the flaps 10 had already been put in and I was not going to make it to runway xx) before I was lined up for runway xy I put the electrical driven fuel pump on and then the engine started back up. I brought the throttle back and told tower I would just land on runway xx. So we landed runway xx and taxied back to the ramp with the fuel pump on. My guess is the engine driven fuel pump had a problem or there was something that clogged the line. The plane was proper preflight and all the fuel sumps were sumped and there was no sign of water or debris.

Original NASA ASRS Text

Title: C172 Instructor reported engine failure during pattern work with student.

Narrative: My student and I were doing pattern work; and we had done 6 touch and goes including 2 slips; simulated engine failure by pulling power to idle and a Go-around. On our last pattern my student pulled power to 1500 rpm abeam the numbers (RWY XX was the runway we were cleared touch and go) the student put in flaps 10 and then turned base. On the base leg I noticed that the RPM indicator showed 1000 rpm so I asked my student why did you pull the power to idle; then I realized the student had not but the engine had failed and in fact the student had given full power and it was still showing 1000 rpm. So I took the controls and noticed the mixture was rich; fuel selector was on both and the fuel shut off value was in. I pitch for best glide and told tower we had an engine failure and asked to land on runway XY. They said I was cleared to land (I chose that runway because the flaps 10 had already been put in and I was not going to make it to runway XX) before I was lined up for runway XY I put the electrical driven fuel pump on and then the engine started back up. I brought the throttle back and told tower I would just land on runway XX. So we landed runway XX and taxied back to the ramp with the fuel pump on. My guess is the engine driven fuel pump had a problem or there was something that clogged the line. The plane was proper preflight and all the fuel sumps were sumped and there was no sign of water or debris.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1681841
Time
Date	201909
Local Time Of Day	0601-1200
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Flight Conditions	VMC
Aircraft 1
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Flight Phase	Final Approach
Route In Use	Visual Approach
Flight Plan	None
Component
Aircraft Component	Engine Driven Pump
Person 1
Function	Instructor
Qualification	Flight Crew Commercial Flight Crew Flight Instructor
Experience	Flight Crew Last 90 Days 112 Flight Crew Total 616 Flight Crew Type 400
Events
Anomaly	Aircraft Equipment Problem Critical