Question $2/20$ Marks in Total$]$

$($a$)$ Determine the time constant for steady pressure to be developed in a circular $10m$ diameter steel michs$-$rube that is $3$ cm long, for water pumped using a $10$ mm diameter glass syringe in a syringe pump, where the syringe travel is $10\%$ of the $150$ mm length of the syringe.

$[10$ Marks$]$

Question $2[20$ Marks in Total$]$

$($a$)$ Determine the time constant for steady pressure to be developed in a circular $10m$ diameter steel micro$-$tube that is $3$ cm long, for water pumped using a $10$ mm diameter glass syringe in a syringe pump, where the syringe travel is $10\%$ of the $150$ mm length of the syringe.

$[10$ Marks$]$

Question $2[20$ Marks in Total$]$

$($a$)$ Determine the time constant for steady pressure to be developed in a circular $10m$ diameter steel micro$-$rube that is $3$ cm long, for water pumped using a $10$ mm diameter glass syringe in a syringe pump, where the syringe travel is $10\%$ of the $150$ mm length of the syringe.

$[10$ Marks$]$

$($b$)$ Comment on how long you should wait before assuming steady conditions.

$[2$ Marks$]$

$($c$)$ Suggest an alternative means to reduce compressibility effects.

$[3$ Marks$]$

HINT: using the following expression for the velocity distribution in the pump, where U is the piston velocity, develop a differential equation in terms of Pressure $($P$)$

$u_p(x,t)=-\frac{1}{K}\frac{dP}{dt}(x-Ut)+U$

set the pressure datum to be zero at the outlet of the tube.

HINT: using the following expression for the velocity distribution in the pump, where U is the piston velocity, develop a differential equation in terms of Pressure $($P$)$

$u_p(x,t)=-\frac{1}{K}\frac{dP}{dt}(x-Ut)+U$

set the pressure datum to be zero at the outlet of the tube.