Final answer:
(a) The resistance of the hose is 8.00 × 10
N s
/m
.
(b) The viscosity of the concrete, assuming laminar flow, is 400 Pa s.
(c) The power being supplied, neglecting the power to increase velocity, is 256 kW.
Explanation:
(a) To determine the resistance of the hose, we can use the Hagen-Poiseuille equation for flow through a cylindrical pipe:
is the resistance,
is the viscosity,
is the length of the hose, and
is the radius. Given the length
diameter
, and pressure
, we find the radius
and then calculate the resistance
.
(b) For laminar flow, the Hagen-Poiseuille equation can be rearranged to solve for viscosity:
Substituting the known values, including the resistance calculated in part (a), we find the viscosity
![\(\eta\).](https://img.qammunity.org/2021/formulas/physics/high-school/3flusc20zcjeg797gbnbn3ux4k2unddauw.png)
(c) To find the power supplied, we can use the formula
, where \
is the flow rate, and
is the pressure difference. Given the flow rate
and pressure
we convert the flow rate to
and calculate the power supplied by the pump.