Dr. Prometheus wants to describe the attitudes of all 18-year-old Houstonians concerning the legalization of marijuana. She rand
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The inlet velocity is 1.4 m/s and inlet volume is 0.019 m³/s.
Explanation:
When water entering the tube of constant diameter flows through the tube, it exhibits continuity of mass in the hydrostatics. So the mass of water moving from the inlet to the outlet tend to be same, but the velocity may differ.
As per mass flow equality which states that the rate of flow of mass in the inlet is equal to the product of area of the tube with the velocity of the water and the density of the tube.
Since, the inlet volume flow is measured as the product of velocity with the area.
Inlet volume flow=Inlet velocity*Area*time
And the mass flow rate is
Mass flow rate in the inlet=density*area*inlet velocity*time
Mass flow rate in the outlet=density*area*outlet velocity*time
Since, the time and area is constant, the inlet and outlet will be same as
(Mass inlet)/(density*inlet velocity)=Area*Time
(Mass outlet)/(density*outlet velocity)=Area*Time
As the ratio of mass to density is termed as specific volume, then
(Specific volume inlet)/(Inlet velocity)=(Specific volume outlet)/(Outlet velocity)
Inlet velocity= (Specific volume inlet)/(Specific volume outlet)*Outlet velocity
As, the specific volume of water at inlet is 0.001017 m³/kg and at outlet is 0.05217 m³/kg and the outlet velocity is given as 72 m/s, the inlet velocity
is
So, the inlet velocity is 1.4035 m/s.
Then the inlet volume will be
As the diameter of tube is 130 mm, then the radius is 65 mm and inlet velocity is 1.4 m/s
So, the inlet volume is 0.019 m³/s.
Thus, the inlet velocity is 1.4 m/s and inlet volume is 0.019 m³/s.
The time taken by the swimmer was 1 hour.
Why?
Since the swimmer is maintaining an angle of 150° while he was swimming, there were two components of the speed (horizontal and vertical). If we want to calculate the time taken by him to cross the river, we need to calculate the vertical speed and consider that the flow's speed is compensated by his horizontal speed.
We can calculate both components of the speed using the following formula:
Now, calculating we have:
Therefore, we have that the horizontal speed is compesating the flow's speed while his vertical speed is used to cross the river which is 1 Km wide.
Hence, we have that the tame taken is:
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