That was exactly how my grandma watered her garden out on the farm.
Out in country on farm, they only had rocker lift pump that pushed water up about 10 ft high, then over in pipe to "Wash House" that had 300 gallon tank in attic to store water. When she wanted to water the garden, she turned diverter valve in flow of water to go to centrifical pump like you have. It had enough pressure to run impulse sprinkler about 50 feet away in the garden. She grew the best red potatoes and tomatoes. Those were the days.
As for original use of that Emerson electric motor, it may have been in old school washing machine . . . . or who knows ??