A given lake can be approximated as a rectangular prism, with dimensions 2 km by 5 km and a depth of 50 m. At one end of the lake, a river with cross-sectional area 50 m brings water into the lake, and at the other end water flows out at a rate of 27.5 m/s. Water evaporates from the lake's surface at a rate of 0.15 m/s per km. (i) (3 marks) If the lake depth remains constant, what is the volumetric flow rate of the river inflow? The river water is warmer than the surrounding lake contents, leading to a horizontal temperature distri- bution just below the surface of where To 10C, AT = 5C, a = inflow just below the surface. = T(x, y) = To + ATe-/ae-y/(26) 50 m, b= 10 m, and the point (x, y) = (0,0) is at the centre of the river (ii) (1 mark) Is this a steady or unsteady temperature distribution? Why? (iii) (3 marks) If fluid parcel A is released at point (0,0) and is advected by a velocity vave in the 2-direction, what is the rate of change of the fluid parcel temperature TA at this location? After a rainy and snowy winter, the flow rate of the river increases to Qin = 35 m/s. (iv) (3 marks) Find the rate at which the lake depth increases with this increased flow rate.