A pipeline with variable cross-section contains water with specific weight
$${10^4}\,\,N/{m^3}.$$ The flow conditions at two points $$1$$ and $$2$$ on the axis of the pipe are:
$$\eqalign{ & {P_1} = 3\,\,bar,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{V_1} = 10\,\,m/s \cr & {P_2} = 1\,\,bar,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{V_2} = 20\,\,m/s \cr} $$

Consider frictional losses to be negligible. For no-flow condition between points $$1$$ and $$2$$ (as shown in Figure), if the height $${z_1}$$ from the datum is $$1$$ $$m,$$ then the height $${z_2}$$ (in $$m$$) is _____________ $$\left( {g = 9.81\,\,m/{s^2}} \right)$$

A metallic cylindrical casing of an exhaust pipe has inner radius $$50$$ $$mm$$ and wall thickness $$7$$ $$mm.$$ If the thermal conductivity of the material of the casing is $$50$$ $$W/m$$-$$K,$$ then the thermal resistance of the casing in $$K/kW$$ is ________________ (up to three decimal places).

In a calendar year, the demand forecast of motorbikes for the month of june is $$200.$$ The actual demand of motorbikes for the month of June and July are $$300$$ and $$350,$$ respectively. If single exponential smoothing method with smoothing constant $$0.7$$ is used, then the demand forecast for the month of August is ___________.

In a project, tasks $$A, B, C, D, E, F, G, H, I$$ and $$J$$ are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.

The time required (in days) to complete the project along the critical path is ______________