Have you measured the dimensions of your existing power supply unit?
The eMachines ET1161-05's case looks like it supports standard ATX form factor power supply units.
Standard ATX12V Power Supply Dimensions:
150mm W x 86mm H x 140mm D
5.9"W x 3.4"H x 5.5"D
The depth is the only spec that will vary usually based on the power supply unit's capacity.
The Corsair Gaming Series GS600 (CMPSU-600G) dimensions are:
150mm(W) x 86mm(H) x 160mm(D)
5.9"W x 3.4"H x 6.3"D