An engineering laboratory experiment uses a triangular weir in an open channel to measure flow rate. The nominal weir angle is \(90^{\circ}\). In a certain test, the head of water above the weir was 4 in. The uncertainty in the weir angle is \(\pm 2^{\circ}\) and the uncertainty in the depth measurement is \(\pm 0.05\) in. Compute the flow rate and the uncertainty in the flow rate.