CRJ700 Captain reported a Hydraulic System 3 failure in flight. After coordinating with with the company; maintenance; and ATC; the crew continued on to the destination and were towed from the runway after landing.

Narrative

I was Pilot Monitoring (PM); and the First Officer was Pilot Flying (PF) for this leg from ZZZ1 to ZZZ2. While climbing between FL200 and FL210; the HYD 3 LO PRESS MASTER CAUTION presented on the EICAS (engine indicating and crew alerting system) primary page. I immediately viewed the HYD synoptic page which indicated a complete loss of hydraulic fluid in system 3 (0%). We made a request to ATC to level off at FL230; explaining that we were having a malfunction with the hydraulic system and would have to accomplish checklists. I transferred radio communications to the First Officer; who was the flying pilot; and I accomplished the appropriate QRH (quick reference handbook) check list (HYD 3 LO PRESS: 4-12). After the QRH items were complete; I declared priority with ATC; indicating that; while we would be conferring with Dispatch and Maintenance; it was our present intention to continue to ZZZ2. I asked the First Officer to decelerate from 280 KTS to 250 KTS to mitigate higher fuel consumption at a lower than planned cruising altitude. I sent an ACARS message to Dispatch and Maintenance; explaining the malfunction and our intentions. I then informed the Flight Attendants to prepare the cabin for a Yellow Level priority; the nature of the priority; and the time remaining (30 minutes). I also informed them that the aircraft would be coming to a complete stop on the runway; would be unable to taxi off; and to expect a tug to tow the aircraft to our gate. Finally; I informed them to expect a firmer than normal landing. We received a response from Dispatch indicating that they were in accord with the decision to continue to ZZZ2 and asking if any other aircraft systems were malfunctioning as well. We replied that only those components associated with Hydraulic System 3 were effected. I then made a passenger announcement; explaining that hydraulic pressure was lost in one of our hydraulic systems and that this malfunction would require us; after landing; to be towed off the runway by a vehicle similar to the vehicle that pushes the aircraft from the gate. I also informed them to expect a landing that is more firm than they might normally be accustomed to. Finally; I requested that the passengers pay close attention to the instructions of the Flight Attendants. We then informed ATC that we would require a minimum of a 15 mile final for Runway XXR; (the longest available runway); and that we would be unable to vacate the runway after landing; but were coordinating with the company to be towed from the runway. ATC acknowledged and also indicated that ARFF (airport rescue and firefighting) would be standing by. All standard briefings and checklists were accomplished. Special attention was given to calculating; verifying; and briefing the approach speed; landing distance; flap setting (20 degrees); and manual gear extension. We also briefed the need for continuous brake application to bring the aircraft to a stop due to the use of accumulator pressure. We were configured; flaps 20; after having intercepted the localizer at a speed of 180KTS. Before glideslope intercept I verified and pulled the landing gear manual release handle and confirmed that both the main landing gear and the nose landing gear were all in the down and locked position. The First Officer slowed to the calculated Vref speed +5 for flaps 20 and we accomplished the Landing Checklist. The First Officer did an exceptional job maintaining the stabilized approach criteria at the appropriate speeds; achieved Vref by 50 feet; flared appropriately; made a normal touchdown at an appropriate rate of descent; and applied the brakes continuously and smoothly. To the passengers; the landing would have felt normal. After the aircraft was brought to a stop and the parking brake was set; the timer was started to shut down an engine. I made a PA; telling the passengers to remain seated with their seat belts securely fastened. The aircraft was immediately met by the tow vehicle andwe were given a discrete frequency to communicate directly with them. We informed the ground crew that; due to a deferred APU; we would be required to leave the right engine running while under tow. After the two minutes had elapsed we shut down the left engine. Shortly thereafter the tow vehicle had captured the aircraft and we were towed to the gate; completing all normal checklists when appropriate. Hydraulic System 3 lost all hydraulic fluid in flight.