Consider a cart as shown, with steady-state conditions having been reached, i.e. the cart has filled to a point where the amount of water inside it remains constant. The diameter of both outlets is given as Do. The water column height at exit 2 is twice that at exit 1, that is, H2 = 2H1. Assume inviscid flow. Assume that cart is on level surface. Clearly mark the CV you are using to answer the following questions and also show your axes. (a) Find expressions for V, and V in terms of the heights H2 and H1 using appropriate conservation law. (b) Using conservation of mass for an appropriate control volume, find relation between the jet velocity V; and exit velocities V and V2 and the pipe diameters Do and D;. (c) If no horizontal force is needed for the cart to be stationary, find a numerical value for Do/Dj. You may have to use the expressions obtained in the previous subparts.

Please answer question in detail subject is fluid mechanics

Consider the two-dimensional flow of an inviscid, incompressible fluid described by the superposition of a parallel flow of velocity V0, a source of strength q, and a sink of strength −q, separated by a distance b in the direction of the parallel flow, the source being upstream of the sink. (a) Find the resultant stream function and velocity potential. (b) Sketch the streamline pattern. (c) Find the location of the upstream stagnation point relative to the source.  

A pipeline of 50 mm diameter and 4.5 km length connects two reservoirs whose constant difference of water level is 12 m. A branch pipe 1.25 km long and taken from a point distance of 1.5 km from reservoir A, leads to reservoir C whose water level is 15 m below that of reservoir A. Find the diameter of the branch pipe so that the flow into both the reservoirs is the same. Assume the coefficient of friction for each pipe, ƒ = 0.0075, and neglect minor losses.