Preliminary force balance:
to get min k value
when plate is closed, spring force needs to overcome weight of water column (1 inch pipe- .0127 m radius)
weight of water column= rhogV= (1000 kg/m^3)(9.81 m/s^2)(pi(0.0127m)^2(2m))= 9.9416 N
originally used displacement of plate= compression of spring but this is not correct since if the spring is originally compressed when the plate is open the total compression of the spring will be that original compression plus the displacement of the plate. After measuring how much the spring is originally compressed (orig. spring length-5 cm, our current spring is 9 cm so 4 cm for this spring) and how much the plate moves (1.3 cm) you can find the total compression of the spring when the plate is closed. For our current spring and setup, this is 5.3 cm.
Fspring= k*0.053= 9.9416 N
k= 187.6 N/m
By measuring the elongation of the spring when a known mass is hung from it we experimentally found a k value of about 71 N/m. We have run the pump with this spring before and experienced different results. We had instances where the plate wouldn't open and after giving it a push it would run for a few cycles. We have also experienced the opposite of this where the plate does not close but after holding it down for a few seconds will run a few cycles. However, we purchased a new middle piece between the experiments and the measurements so new tests have to be run to see how the pump acts with this spring and the new middle piece. Additionally, we can look into purchasing (or finding) springs with k values near but slightly above the minimum calculated value either for their length or find springs with the same length as the one we did the measurements for.
Preliminary force balance: to get min k value when plate is closed, spring force needs to overcome weight of water column (1 inch pipe- .0127 m radius) weight of water column= rhogV= (1000 kg/m^3)(9.81 m/s^2)(pi(0.0127m)^2(2m))= 9.9416 N originally used displacement of plate= compression of spring but this is not correct since if the spring is originally compressed when the plate is open the total compression of the spring will be that original compression plus the displacement of the plate. After measuring how much the spring is originally compressed (orig. spring length-5 cm, our current spring is 9 cm so 4 cm for this spring) and how much the plate moves (1.3 cm) you can find the total compression of the spring when the plate is closed. For our current spring and setup, this is 5.3 cm. Fspring= k*0.053= 9.9416 N k= 187.6 N/m
By measuring the elongation of the spring when a known mass is hung from it we experimentally found a k value of about 71 N/m. We have run the pump with this spring before and experienced different results. We had instances where the plate wouldn't open and after giving it a push it would run for a few cycles. We have also experienced the opposite of this where the plate does not close but after holding it down for a few seconds will run a few cycles. However, we purchased a new middle piece between the experiments and the measurements so new tests have to be run to see how the pump acts with this spring and the new middle piece. Additionally, we can look into purchasing (or finding) springs with k values near but slightly above the minimum calculated value either for their length or find springs with the same length as the one we did the measurements for.