The question involves calculating the fluid flow rate using the equation Q = A × v, where Q is flow rate, A is the cross-sectional area, and v is velocity. Factors such as fluid density, pressure difference, viscosity, tube length, and radius directly impact the flow rate, illustrating fluid dynamics principles.
The question asks about the fluid flow rate out of a sphere given a fluid density and a velocity field. To find the flow rate, we use the fact that the mass flow rate is the product of fluid density (p), cross-sectional area (A), and the magnitude of the velocity (v). Given the flow rate equation Q = A × v, where Q is the flow rate, A is the cross-sectional area, and v is the velocity, we can calculate the flow rate for different conditions in fluid dynamics.
(a) To find the flow rate in liters per second of water moving through a hose with an internal diameter of 1.60 cm at a velocity of 2.00 m/s, we calculate the area, convert the units appropriately, and multiply by the velocity.
(b) The fluid velocity's relationship with the nozzle's diameter is inversely proportional. If the velocity in the nozzle is 15.0 m/s, we can determine the nozzle's inside diameter using the continuity equation and the given fluid velocities and diameters.
Given a scenario of fluid flowing at a specific rate through a tube, various factors can alter the flow rate. Changes in pressure difference, fluid viscosity, tube length, and tube radius will affect the flow rate differently. For instance, if the pressure difference increases, the flow rate will likely increase, whereas an increase in fluid viscosity or tube length will decrease the flow rate. A smaller tube radius will also decrease the flow rate. All these factors show the sensitivity of flow rate to changes in the conditions of fluid flow.